home‎ > ‎4.3‎ > ‎

4.3.7 - xec_numbers

4.3.7
Extended Cascading-E Numbers
Part I
(5110 - 7399)

 
                    Now that I have established Extensible-E up to φ(ω,0,0, let's take it out for a spin and forge a plethora of new googolism's in xE^ ...
                    
                        Ready for the next next level ...


Forging xE^ Numbers

          
                    The following catalog of googolism's is MASSIVE! The list contains googolism's #5110 through #15610. This works out to exactly 10,501 googolism's organized into 29 new regiments, each regiment containing several hundred googolism's alone.This dwarfs the previous output of E#,xE#, and E^ combined. There is more than twice the number of xE^ googolism's compare to the sum of E#,xE# and E^ googolism's!

                    In addition there are 2 beta-release regiments totaling 568 additional numbers, 262 of which are named. This provides a sneak peak into the next level of development for ExE.
 
                    I should note that not all of these googolism's name unique numbers. Some numbers can have 2 or more names because they have several possible constructions within my naming-system. I've also taken the liberty to rebrand certain numbers to suit the new developments in xE^. Not all names I've come up with over the years are counted either. Names which have been discontinued are not amongst the counted.
 
                    Despite my (futile) attempt to be exhaustive here, the number of numbers constructible within my naming-system would be vastly larger. I could have easily expanded some of the blocks into several blocks of their own. Even then this would not be an exhaustive list. But even if we considered every name legally constructible within my naming scheme ... the gaps between any two distinct numbers are so monstrously vast and beyond our grasp that all we can say is they must contain as many numbers as the size of the endpoints themselves! The eldritch abominations truly outnumber our puny millions,billions, and trillions, a blasphemorgulus to one!!! 
 
On that note let's begin ... we've got a long way to go ...



PART I

(5110 - 7399)


 
Tethrathoth Regiment

Category 58
Members: 498
(5110 - 5607)


φ(1,0)



                    We can begin more or less exactly where we left off with Cascading-E Notation (E^) and Limited Extension Cascading-E Notation (LECEN), except with a greater clarity than before.

                    Just as before we can define:

(5110) tethrathoth = E100#^^#100

( also (5111) thoth )

                    The transformation laws conveniently support this definition via Law II.A under the definition of fundamental sequences. Note that Law II.A is essentially the same rule that Aarex uses at the outset of his article of Extended Cascading-E:

#^...^(#...#) = #^...(#^...^(#...)) 
                    
                        ... but there are some key differences. Firstly, it only defines this sequence if the polyponent is a single hyperion. Law II.A does not apply in situations such as #^^##. Secondly, while it seems more restrictive than Aarex's rule it's actually vastly more general:

&(α)^..k..^(#)[1] = &α

&(α)^..k..^(#)[n] = &(α)^..k-1..^((α)^..k..^(#)[n-1])

                        ... here the polybase is not restricted to just a hyperion. Rather it can be any member of the set of legal delimiters, namely the set x^. Typically this will be an epsilon number, though the rules allow the possibility of any legal delimiter being used, leading to hosts of rogues such as ##^^# for example. In this case it expands as expected...

##^^# --> ##^##^...^##^## --> ##^##^...^(##^#*##^#*...*##^#*##^#) -->

##^##^...^(##^#*##^#*...*##^#*##*##*...*##*##)

                        This is not so strange or un-intuitive and leads to a lot of potential freedom. There is a third key difference. My rule is actually a fundamental sequence, where is Aarex's rule is not. Notice this transformation is applied regardless of what the last argument actually is. The rule is a synonym substitution, not a fundamental sequence. To give an example...

@100#^^###n = @100#^#^^##n = @100#^#^#^^#n 

                         This same sequence is carried out regardless of what "n" actually is. Note that the rule doesn't terminate. It doesn't specify a base case, leading to the meaningless transformation 

#^^# = #^#^^

                        Aarex does however state a base case elsewhere as #^^# = #^#. These leads to a slightly inelegant set of synonyms...

#^^# = #^#

#^^## = #^#^#

#^^### = #^#^#^#

                        In this instances we see clearly that we are dealing with synonyms here, not fundamental sequences, because this is not an equality of numeric expressions in ExE, but rather an equality of delimiters. The use of synonyms however is wasteful here as we can simply use #^^#[n] to represent the entire sequence Aarex is trying to describe! Another reason this does not seem like a good choice is that it breaks a nice symmetry we have used up to this point. Every time we are applying a fundamental sequence to a hyperion limit ordinal we can interpret it as substituting a numeric value for the keystone hyperion. For example...

#^#[n] = #^(n) = ###...## w/n #s

#^##[n] = #^(#*(n)) = #^#*#^#*...*#^# w/n #^#s

                        So note that we can interpret hyperion tetration in the following way:

#^^#[n] = #^^(n) = #^#^^(n-1) = #^#^#^^(n-2) = ... = #^#^#^...^#^# w/n #s

                    In essence, a hyperion is just a variable container which can be replaced by any positive integer. Aarex, on the other hand, treats them as simple counters, ie:

# = 1

## = 2

### = 3

etc.

                    If that were so we'd have:

#^# = #

#^## = ##

#^### = ###

etc.

                    but then hyperion exponentiation would have no effect. This usage is inconsistent with the rest of Extensible-E. Although Extensible-E conventionally avoids the mixing of numbers and hyperions, the mixing has always been implied since the inception of Cascading-E. For example ...

#1 = #

#2 = ##

#3 = ###

etc.

                    Furthermore, it was implicit in the operation of E^ that # acted as a symbol for a general number. ie #^# really means # raised to any positive integer power. With that in mind let us proceed.

                    Firstly let's check to make sure that our rules do properly evaluate tethrathoth:

E100#^^#100 

= E100#^^#[100]100 

= E100#^(#^^#[99])100 

= E100#^#^(#^^#[98])100

E100#^#^#^(#^^#[97])100

...

E100#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#
^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
#^#^#^#^#^#^#^#^#^#^#^#^#^(#^^#[1])100

= E100#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#
^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^#^
#^#^#^#^#^#^#^#^#^#^#^#^#^#100

                    As you can see it behaves as expected. The #^^# delimiter is the earliest example for the application of rule II.A. 

                Note that Aarex defines this number as E100#^^#^#100. However according to his definitions , since #^^# = #^#, #^^## = #^#^#, #^^### = #^#^#^#, and in general #^^#n = #^^(n+1) it follows that E100#^^#^#100 = E100#^^#^#[100]100 = E100#^^#^(100)100 = E100#^^(101)100. Thus E100#^^#^#100 is actually equal to E100#^^#101 in xE^. This is actually the 101st member of the sequence {grangol,godgahlah,godgathor,godtothol,...}. I'll use a new -toth operator to allow a continuation...

(5112) tethrathothitoth = E100#^^#101

(5113) tethrathothi-dutoth = E100#^^#102

(5114) tethrathothi-tritoth = E100#^^#103 

(5115) tethrathothi-tertoth = E100#^^#104

(5116) tethrathothi-petoth = E100#^^#105

(5117) tethrathothi-extoth = E100#^^#106

(5118) tethrathothi-eptoth = E100#^^#107

(5119) tethrathothi-octoth = E100#^^#108

(5120) tethrathothi-entoth = E100#^^#109

(5121) tethrathothi-dektoth = E100#^^#110

                    ... much much much further in the sequence we have ...

(5122) grand tethrathothE100#^^#100#2 

                     That's the tethrathoth member of the #^^#-sequence! As for evaluating it we first consider the rules and look for the earliest rule which applies: The Base Rule doesn't apply because there is more than 1 argument, The Decomposition Rule doesn't apply since '#' is not an element of x^_lim, the Terminating Rule doesn't apply because the last argument isn't 1, and the Expansion Rule doesn't apply because the last delimiter is '#'. Therefore the Recursive Rule must apply. Here I'll demonstrate the validity of the Rule:

@m#n = @(@m#(n-1))

Let @ = 'E100#^^#'

m = 100

n = 2

Therefore:

E100#^^#100#2 = E100#^^#(E100#^^#100#(2-1)) = E100#^^#(E100#^^#100#1)

We again go through the rules again, but this time applying them to the nested expression: the Base Rule doesn't apply because there is more than 1 argument, the Decomposition Rule doesn't apply because '#' is not a member of x^_lim, the Terminating Rule does apply since the last argument = 1. Again I'll demonstrate the validity of the rule:

@m&1 = @m

Let @ = 'E100#^^#'

m = 100

Therefore:

E100#^^#(E100#^^#100#1) = E100#^^#(E100#^^#100) = E100#^^#(tethrathoth)

                Assuming we have finished the evaluation of tethrathoth (something which is quite impossible in practice, but we can speak in hypothetical terms) the next rule to apply would be the decomposition rule since '#^^#' is a member of x^_lim. Since '#^^#' is of the general form (α)^..k..^(β) , Ruleset II applies, and since β = #, Rule II.A applies:

E100#^^#(tethrathoth) = E100#^^#[tethrathoth]100 

= E100#^(#^^#[tethrathoth-1])100

= E100#^#^(#^^#[tethrathoth-2])100

= E100#^#^#^(#^^#[tethrathoth-3])100

... ... ... ... (you don't even want to know how long) ... ... ... ...

= E100#^#^#^#^#^#^#^#^#^ ... ... ... ... (ditto) ... ... ... ... ^#^#^#^#^#^#^#100

w/tethrathoth #s

                As you can see the 5 rules nicely codify xE^. In fact, these rules are the 
5 fundamental laws of Extensible-E. What this means is that these rules never change. As long as we can keep defining larger hyperion sets and define their fundamental sequences we can continue to expand Extensible-E. This also means that we won't really need to specify them over and over again from this point on and they can be taken as a given.

                    We can also introduce a gong version of a tethrathoth (as was done in the Cascading-E article)...

(5123) tethrathothigong = E100,000#^^#100,000

as well as a grand version for this number...

(5124) grand tethrathothigong = E100,000#^^#100,000#2

                The ' grand ' operator should be very familiar at this point, and we can easily define (5125) grand grand tethrathoth, (5126) grand grand grand tethrathoth, (5127) grand grand grand grand tethrathoth, (5128) grand grand grand grand grand tethrathoth, (5129) grand grand grand grand grand grand tethrathoth, etc. This is where the ' ex ' operator comes in handy. The number proceeding ' ex ' tells us how many times the following element is to be repeated. Example:

(5130) two-ex-grand tethrathoth = grand grand tethrathoth

(5131) three-ex-grand tethrathoth grand grand grand tethrathoth

(5132) four-ex-grand tethrathoth = grand grand grand grand tethrathoth

etc.

thus we can define ...

grand grand tethrathoth = E100#^^#100#3

grand grand grand tethrathoth = E100#^^#100#4

grand grand grand grand tethrathoth = E100#^^#100#5

(5133) five-ex-grand tethrathoth = E100#^^#100#6

(5134) six-ex-grand tethrathoth = E100#^^#100#7

(5135) seven-ex-grand tethrathoth = E100#^^#100#8

(5136) eight-ex-grand tethrathoth = E100#^^#100#9

(5137) nine-ex-grand tethrathoth = E100#^^#100#10

(5138) ten-ex-grand tethrathoth = E100#^^#100#11

...

                This sequence forms the tethrathoth sequence which forms the basis of the continuation into Extended Cascading-E. We can append any number of grand's before tethrathoth that we are capable of constructing. Using the ex-operator the following googolism's can easily be defined:

(5139) hundred-ex-grand tethrathoth = E100#^^#100#101

(5140) googol-ex-grand tethrathoth = E100#^^#100#(1+E100)

(5141) grangol-ex-grand tethrathoth = E100#^^#100#(1+E100#100)

(5142) greagol-ex-grand tethrathoth = E100#^^#100#(1+E100#100#100)

(5143) gigangol-ex-grand tethrathoth = E100#^^#100#(1+E100#100#100#100)

(5144) gorgegol-ex-grand tethrathoth = E100#^^#100#(1+E100##5)

(5145) gulgol-ex-grand tethrathoth = E100#^^#100#(1+E100##6)

(5146) gaspgol-ex-grand tethrathoth = E100#^^#100#(1+E100##7)

(5147) ginorgol-ex-grand tethrathoth = E100#^^#100#(1+E100##8)

(5148) gargantuul-ex-grand tethrathoth = E100#^^#100#(1+E100##9)

(5149) googondol-ex-grand tethrathoth = E100#^^#100#(1+E100##10)

(5150) gugold-ex-grand tethrathoth = E100#^^#100#(1+E100##100)

(5151) gugolthra-ex-grand tethrathoth = E100#^^#100#(1+E100###3)

(5152) gugoltesla-ex-grand tethrathoth = E100#^^#100#(1+E100###4)

(5153) gugolpeta-ex-grand tethrathoth = E100#^^#100#(1+E100###5)

(5154) gugolhexa-ex-grand tethrathoth = E100#^^#100#(1+E100###6)

(5155) gugolhepta-ex-grand tethrathoth = E100#^^#100#(1+E100###7)

(5156) gugolocta-ex-grand tethrathoth = E100#^^#100#(1+E100###8)

(5157) gugolenna-ex-grand tethrathoth = E100#^^#100#(1+E100###9)

(5158) gugoldeka-ex-grand tethrathoth = E100#^^#100#(1+E100###10)

(5159) throogol-ex-grand tethrathoth = E100#^^#100#(1+E100###100)

(5160) tetroogol-ex-grand tethrathoth = E100#^^#100#(1+E100####100)

(5161) pentoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#5)

(5162) hexoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#6)

(5163) heptoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#7)

(5164) ogdoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#8)

(5165) entoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#9)

(5166) dektoogol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#10)

(5167) godgahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#100)

(5168) gridgahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^##100)

(5169) kubikahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^###100)

(5170) quarticahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^####100)

(5171) quinticahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#5)

(5172) sexticahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#6)

(5173) septicahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#7)

(5174) octicahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#8)

(5175) nonicahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#9)

(5176) decicahlah-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#10)

(5177) godgathor-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#100)

(5178) godtothol-ex-grand tethrathoth = E100#^^#100#(1+E100#^#^#^#100)

(5179) godtertol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#5)

(5180) godtopol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#6)

(5181) godhathor-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#7)

(5182) godheptol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#8)

(5183) godoctol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#9)

(5184) godentol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#10)

(5185) goddekathol-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#11)

(5186) tethrathoth-minus-one-ex-grand tethrathoth = E100#^^#100#1#2

(5187) tethrathoth-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#100)

(5188) grand-tethrathoth-ex-grand tethrathoth = E100#^^#100#(1+E100#^^#100#2)

(5189) grand-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#3)

(5190) grand-grand-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#4)

(5191) grand-grand-grand-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#5)

(5192) five-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#6)

(5193) six-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#7)

(5194) seven-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#8)

(5195) eight-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#9)

(5196) nine-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#10)

(5197) ten-ex-grand-tethrathoth-ex-grand tethrathoth
= E100#^^#100#(1+E100#^^#100#11)

(5198) tethrathoth-ex-grand tethrathoth-ex-grand tethrathoth 

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100))

(5199) grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#2))

(5200) grand-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#3))

(5201) grand-grand-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#4))

(5202) grand-grand-grand-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#5))

(5203) five-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#6))

(5204) six-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#7))

(5205) seven-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#8))

(5206) eight-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#9))

(5207) nine-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#10))

(5208) ten-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#11))

...

(5209) tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100)))

(5210) tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-
tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#
(1+E100#^^#100#(1+E100#^^#100))))

(5211) tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-
tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#
(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100)))))

(5212) 
tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth

= E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100#(1+E100#^^#100))))
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))


(5213) 
tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth
w/tethrathoth tethrathoth's

(5214)
tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth tethrathoth's

(5215)
tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's

... ... ... ...

... ... ... ...

w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth-ex-grand-tethrathoth- ... ... -ex-grand-tethrathoth tethrathoth's
w/tethrathoth tethrathoth's

( where there are tethrathoth lines )

                    This is of coarse just a primitive recursive extension so let's move on. We can notate the nth member of the tethrathoth sequence as E100#^^#100#n. The 100th member of the tethrathoth sequence would be E100#^^#100#100. Notice that if we let @ = 'E100#^^#' , we can write @100#100. This looks similar to grangol (E100#100). From this I coined the name grantethrathoth from grangol tethrathoth. The problem is that generalizing this leads to potential problems. To allow for greater and easier generalization I will introduce the carta-operator (from the greek root carta, meaning map)Let G and H be googolism's in ExE. Let H be represented by @100. Let G be represented as E%. Then define G-carta-H as @%. Here is being mapped to H. That is, we can imagine H as the 100th member of some sequence. We can map googol to this by treating it as the 100th member of the sequence 10,100,1000,10000,...etc. This analogy allows us to map any of the googolism's to our new sequence H. Think of @n as a function. @100#100 means grangol mapped to the function @n. This makes completely routine many of the previous googolism's mentioned in the Cascading-E article. Here are some examples:

(5216) grangol-carta-tethrathoth = (5217) grantethrathoth = E100#^^#100#100
( alternatively (5218) ninety-nine-ex-grand tethrathoth )

(5219) greagol-carta-tethrathoth = (5220) greatethrathoth = E100#^^#100#100#100

(5221) gigangol-carta-tethrathoth = (5222) gigantethrathothE100#^^#100#100#100#100

(5223) gorgegol-carta-tethrathoth = (5224) gorgetethrathoth 
E100#^^#100##5

(5225) gulgol-carta-tethrathoth = (5226) gultethrathoth 
= E100#^^#100##6

(5227) gaspgol-carta-tethrathoth = (5228) gasptethrathoth 
= E100#^^#100##7

(5229) ginorgol-carta-tethrathoth = (5230) ginortethrathoth 
= E100#^^#100##8

(5231) gargantuul-carta-tethrathoth = (5232) gargantethrathoth
= E100#^^#100##9

(5233) googondol-carta-tethrathoth = (5234) googontethrathoth
= E100#^^#100##10

                    This is the point at which I stopped in the previous article. The main reason was that the above pattern does not make it readily apparent how gugold and those after it should be appended to tethrathoth. Aarex took this opportunity to attempt to continue the pattern. I'll offer my own continuation below:

(5235) gugolda-carta-tethrathoth = E100#^^#100##100

(5236) graatagolda-carta-tethrathoth = E100#^^#100##100#100

(5237) greegolda-carta-tethrathoth = E100#^^#100##100#100#100

(5238) grinningolda-carta-tethrathoth = E100#^^#100##100#100#100#100

(5239) gugolthra-carta-tethrathoth = E100#^^#100##100##100

(5240) gugoltesla-carta-tethrathoth = E100#^^#100##100##100##100

(5241) throogola-carta-tethrathoth = E100#^^#100###100

(5242) throotrigola-carta-tethrathoth E100#^^#100###100###100

(5243) tetroogola-carta-tethrathoth E100#^^#100####100

...

(5244) godgahlah-carta-tethrathoth = E100#^^#100#^#100

(5245) grand godgahlah-carta-tethrathoth = E100#^^#100#^#100#2

(5246) grangahlah-carta-tethrathoth = E100#^^#100#^#100#100

(5247) greagahlah-carta-tethrathoth = E100#^^#100#^#100#100#100

(5248) gigangahlah-carta-tethrathoth = E100#^^#100#^#100#100#100#100

(5249) gorgegahlah-carta-tethrathoth = E100#^^#100#^#100##5

(5250) gulgahlah-carta-tethrathoth = E100#^^#100#^#100##6

(5251) gaspgahlah-carta-tethrathoth = E100#^^#100#^#100##7

(5252) ginorgahlah-carta-tethrathoth = E100#^^#100#^#100##8

(5253) gugoldgahlah-carta-tethrathoth = E100#^^#100#^#100##100

(5254) gugolthragahlah-carta-tethrathoth = E100#^^#100#^#100##100##100

(5255) gugolteslagahlah-carta-tethrathoth = E100#^^#100#^#100##100##100##100

(5256) throogahlah-carta-tethrathoth = E100#^^#100#^#100###100

(5257) tetroogahlah-carta-tethrathoth = E100#^^#100#^#100####100

(5258) gotrigahlah-carta-tethrathoth = E100#^^#100#^#100#^#100

(5259) gotergahlah-carta-tethrathoth = E100#^^#100#^#100#^#100#^#100

...

(5260) godgoldgahlah-carta-tethrathoth = E100#^^#100#^#*#100

( alternatively (5261) godgahlah-by-hyperia-carta-tethrathoth )

(5262) godthroogahlah-carta-tethrathoth = E100#^^#100#^#*##100

( alternatively (5263) godgahlah-by-deuterhyperia-carta-tethrathoth )

(5264) godtetroogahlah-carta-tethrathoth = E100#^^#100#^#*###100

( alternatively (5265) godgahlah-by-tritohyperia-carta-tethrathoth )

...

(5266) deutero-godgahlah-carta-tethrathoth = E100#^^#100#^#*#^#100

(5267) trito-godgahlah-carta-tethrathoth  E100#^^#100#^#*#^#*#^#100

(5268) teterto-godgahlah-carta-tethrathoth = E100#^^#100#^#*#^#*#^#*#^#100

...

(5269) gridgahlah-carta-tethrathoth = E100#^^#100#^##100

(5270) kubikahlah-carta-tethrathoth = E100#^^#100#^###100

(5271) quarticahlah-carta-tethrathoth = E100#^^#100#^####100

...

(5272) godgathor-carta-tethrathoth = E100#^^#100#^#^#100

(5273) gralgathor-carta-tethrathoth = E100#^^#100#^#^##100

(5274) godtothol-carta-tethrathoth = E100#^^#100#^#^#^#100

...

                    ... this brings us to (5275) tethrathoth-carta-tethrathoth , E100#^^#100#^^#100, also called tethratrithothThis leads to an even faster diagonalization...

(5276) tethratrithoth = E100#^^#100#^^#100

(5277) tethraterthoth = E100#^^#100#^^#100#^^#100

(5278) tethrapethoth = E100#^^#*#5

(5279) tethra-exthoth = E100#^^#*#6

(5280) tethra-epthoth = E100#^^#*#7

(5281) tethra-octhoth = E100#^^#*#8

(5282) tethra-ennthoth = E100#^^#*#9

(5283) tethra-dekathoth = E100#^^#*#10

...

                    This leads to another level of diagonalization even more ridiculous...

(5284) tethrathoth-by-hyperion = E100#^^#*#100 

(5285) tethrathoth-by-deutero-hyperion = E100#^^#*##100 

(5286) tethrathoth-by-trito-hyperion = E100#^^#*###100

(5287) tethrathoth-by-teterto-hyperion = E100#^^#*####100

(5288) tethrathoth-by-pepto-hyperion = E100#^^#*#^#5

(5289) tethrathoth-by-exto-hyperion = E100#^^#*#^#6

(5290) tethrathoth-by-epto-hyperion = E100#^^#*#^#7

(5291) tethrathoth-by-ogdo-hyperion = E100#^^#*#^#8

(5292) tethrathoth-by-ento-hyperion = E100#^^#*#^#9

(5293) tethrathoth-by-dekato-hyperion = E100#^^#*#^#10


...


(5294) tethrathoth-by-godgahlah = E100#^^#*#^#100

(5295) tethrathoth-by-godgahlah-by-hyperion = E100#^^#*#^#*#100 

(5296) tethrathoth-by-deutero-godgahlah = E100#^^#*#^#*#^#100 

(5297) tethrathoth-by-gridgahlah = E100#^^#*#^##100

 (5298) tethrathoth-by-kubikahlah E100#^^#*#^###100

(5299) tethrathoth-by-quarticahlah = E100#^^#*#^####100

(5300) tethrathoth-by-quinticahlah = E100#^^#*#^#^#5

(5301) tethrathoth-by-sexticahlah = E100#^^#*#^#^#6

(5302) tethrathoth-by-septicahlah = E100#^^#*#^#^#7

(5303) tethrathoth-by-octicahlah = E100#^^#*#^#^#8

(5304) tethrathoth-by-nonicahlah = E100#^^#*#^#^#9

(5305) tethrathoth-by-decicahlah = E100#^^#*#^#^#10 

(5306) tethrathoth-by-godgathor = E100#^^#*#^#^#100

 (5307) tethrathoth-by-godtothol E100#^^#*#^#^#^#100

(5308) tethrathoth-by-godtertol = E100#^^#*#^^#5

(5309) tethrathoth-by-godtopol = E100#^^#*#^^#6

(5310) tethrathoth-by-godhathor = E100#^^#*#^^#7

(5311) tethrathoth-by-godheptol = E100#^^#*#^^#8

(5312) tethrathoth-by-godoctol = E100#^^#*#^^#9

(5313) tethrathoth-by-godentol = E100#^^#*#^^#10

(5314) tethrathoth-by-goddekathol = E100#^^#*#^^#11

...

                    This eventually leads to E100#^^#*#^^#100. Here we have the hyperion-power operatorsdeutero, trito, teterto, etc. These take any hyper-factor, &, and then replace it with &^(n). Where deutero = 2 , trito = 3, teterto = 4, etc.
Thus we have:

(5315) deutero-tethrathoth = E100#^^#*#^^#100 = E100(#^^#)^#2

(5316) trito-tethrathoth = E100#^^#*#^^#*#^^#100 = E100(#^^#)^#3

(5317) teterto-tethrathoth = E100#^^#*#^^#*#^^#*#^^#100 = E100(#^^#)^#4

(5318) pepto-tethrathoth = E100(#^^#)^#5

(5319) exto-tethrathoth = E100(#^^#)^#6

(5320) epto-tethrathoth = E100(#^^#)^#7

(5321) ogdo-tethrathoth = E100(#^^#)^#8

(5322) ento-tethrathoth = E100(#^^#)^#9

(5323) dekato-tethrathoth = E100(#^^#)^#10 

...

 (5324) hecato-tethrathoth = E100(#^^#)^#100

                    Aarex dubs the hecato-tethrathoth the 'tethrathor'. His definition however differs significantly, so let's examine it:

'tethrathor' = E100#^(#^^(#^#/#)*#)100

                    The idea here is actually quite interesting. He uses the /# to avoid the problem that occurs in the ordinal ω^(ε0+1) of offset (see article 4.2.5). We can define /# as hyperion division, something I already suggested in the previous article as a way to define E^. Here is how this would be evaluated...

E100#^(#^^(#^#/#)*#)100 = E100(#^(#^^(#^#/#))^(100)100 =

E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^#/#)100

E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^(100)/#)100

E100(#^(#^^(#^#/#))^(99)*#^(#^^(#^99))100

E100(#^(#^^(#^#/#))^(99)*#^(#^^100)100

E100(#^(#^^(#^#/#))^(99)*#^^(101)100

                    As you can see there is still an offset created by this system. However, to be fair, things are functional up to this point. Interestingly enough, xE^ also can support this format, even though the rules were not designed to. It's part of the rogue set of delimiters. For example:

E100#^(#^^#*#)100

                    By Rule I.B we have that # is being raised to a successor. So following the rule we get...
                    
E100#^(#^^#*#)100 = E100(#^(#^^#))^(100)100 =

E100(#^(#^^#))^(99)*#^#^^#100

= E100(#^(#^^#))^(99)*#^#^^(100)100

= E100(#^(#^^#))^(99)*#^^(101)100

                    Although the rules allow for the cantor normal forms, it has the same problem as well ... it has a slight offset. This is part of why I have opted for the more natural extension of stacking epsilon numbers. I should also note that E100(#^^(101))^#100 is not the same thing as E100#^(#^^#*#)100 even if they seem like they should be the same. The reason for this is that #^^(101) is a E^ delimiter, where as #^^# is a xE^ delimiter. They behave very differently, and #^^# has a much faster growing fundamental sequence, although it takes a while to catch up. Remember that in the case of E100#^(#^^#*#)100, we are actually getting 100 iterations of #^(#^^#) not #^(#^^100). Rather, only the last one becomes #^(#^^100). It's a long time before the 2nd to last gets it's turn. By the time it does the final argument has become mind-bogglingly massive, call it X. The 2nd to last then becomes #^(#^^X) = #^^(X+1). The +1 is an additional offset. Each #^(#^^#) will add 1 to the height of the hyperion power tower. Mind you, the effect is negligible, but it does guarantee that E100(#^^#)^#100 < E100#^(#^^#*#)100 , even though ordinal arithmetic would tell us these ordinals, (#^^#)^# and #^(#^^#*#), are the same. In any case I'll appropriate this interesting case and say:

(5325) tethrathor = E100#^(#^^#*#)100

                    There is a way to correct this problem. Define #-1 such that #-1[n] = #[n]-1. Treating # as a indefinite value, rather than as ω, allows for much more flexibility. We can then actually define...

hecato-tethrathoth = E100#^(#^^(#-1)*#)100

                    This was the meaning Aarex was going for. I should note that this is an illegal delimiter not strictly supported by the rules of xE^. However it isn't difficult to tweak them a bit to allow such forms. Here is how this would be evaluated...

E100#^(#^^(#-1)*#)100 =

E100(#^(#^^(#-1)))^(100)100

= E100(#^(#^^(#-1))^(99)*#^(#^^(#-1))100

E100(#^(#^^(#-1))^(99)*#^(#^^(100-1))100

E100(#^(#^^(#-1))^(99)*#^(#^^(99))100

E100(#^(#^^(#-1))^(99)*#^^(100)100

                        This little correction factor will propagate throughout the expression and evaluation process.

                    Although this is the standard progression used past ε(0) in the fast growing hierarchy, I find the offset to be somewhat unnatural. This is why I have opted instead for the stacking sequence, that treats ε(0) as a new base on which to stack ordinal exponents. The two forms leads to slightly different functions unless a correction factor is implemented as above. 

Aarex's terms from the 'tethrathor' group to the 'todatriath' group lie below 
ε(1). I did not coin any googolism's in the range between hecato-tethrathoth, and Monster-Giant. Here I'll provide some terms:

(5326) tethrafact = E100(#^^#)^#100

(from tetration + factor because #^^# is the only factor of the hyper-product)

alternatively (5327) tethrachain

( also hecato-tethrathoth )

(5328) grand tethrafact = E100(#^^#)^#100#2 = E100(#^^#)^#tethrafact

( also (5329) grand hecato-tethrathoth )

(5330) tethratrifact = E100(#^^#)^#100(#^^#)^#100

(5331) deutero-tethrafact = E100(#^^#)^#*(#^^#)^#100 = E100(#^^#)^##2

(5332) trito-tethrafact = E100(#^^#)^##3

(5333) teterto-tethrafact = E100(#^^#)^##4

(5334) pepto-tethrafact = E100(#^^#)^##5

(5335) exto-tethrafact = E100(#^^#)^##6

(5336) epto-tethrafact = E100(#^^#)^##7

(5337) ogdo-tethrafact = E100(#^^#)^##8

(5338) ento-tethrafact = E100(#^^#)^##9

(5339) dekato-tethrafact = E100(#^^#)^##10

...

(5340) grideutertethrathoth = E100(#^^#)^##100

alternatively (5341) tethrathothigrid

(5342) kubicutethrathoth
 = E100(#^^#)^###100

alternatively (5343) tethrathothicube

(5344) quarticutethrathoth = E100(#^^#)^####100

alternatively (5345) tethrathothitess

(5346) quinticutethrathoth = E100(#^^#)^#^#5

alternatively (5347) tethrathothipent

(5348) sexticutethrathoth = E100(#^^#)^#^#6

alternatively (5349) tethrathothihex

(5350) septicutethrathoth = E100(#^^#)^#^#7

alternatively (5351) tethrathothihept

(5352) octicutethrathoth = E100(#^^#)^#^#8

alternatively (5353) tethrathothi-ogd

(5354) nonicutethrathoth = E100(#^^#)^#^#9

alternatively (5355) tethrathothi-enn

(5356) decicutethrathoth = E100(#^^#)^#^#10

alternatively (5357) tethrathothideck

...

(5358) centicutethrathoth = E100(#^^#)^#^#100

alternatively (5359) tethrathothihect

                        ... but this isn't nearly extensible enough, and we want more ... many many more intermediate terms before we get up to Monster-Giant. See if you can figure out these constructions ...

(5360) tethragodgathor = E100(#^^#)^#^#100

alternatively (5361) tethrathoth-ad-godgahlahium

(5362) tethragralgathor = E100(#^^#)^#^##100

alternatively (5363) tethrathoth-ad-gridgahlahium

(5364) tethrathraelgathor = E100(#^^#)^#^###100

alternatively (5365) tethrathoth-ad-kubikahlahium

(5366) tethraterinngathor = E100(#^^#)^#^####100

alternatively (5367) tethrathoth-ad-quarticahlahium

(5368) tethrapentaelgathor = E100(#^^#)^#^#^#5

alternatively (5369) tethrathoth-ad-quinticahlahium

( formally tethrapehaelgathor )

(5370) tethrahexaelgathor = E100(#^^#)^#^#^#6

alternatively (5371) tethrathoth-ad-sexticahlahium

(5372) tethraheptaelgathor = E100(#^^#)^#^#^#7

alternatively (5373) tethrathoth-ad-septicahlahium

(5374) tethra-octaelgathor = E100(#^^#)^#^#^#8

alternatively (5375) tethrathoth-ad-octicahlahium

(5376) tethra-ennaelgathor = E100(#^^#)^#^#^#9

alternatively (5377) tethrathoth-ad-nonicahlahium

(5378) tethra-dekaelgathor = E100(#^^#)^#^#^#10

alternatively (5379) tethrathoth-ad-decicahlahium

...


(5380) tethragodtothol = E100(#^^#)^#^#^#100

alternatively (5381) tethrathoth-ad-godgathorium

(5382) tethragraltothol = E100(#^^#)^#^#^##100

alternatively (5383) tethrathoth-ad-gralgathorium

(5384) tethrathraeltothol = E100(#^^#)^#^#^###100

alternatively (5385) tethrathoth-ad-thraelgathorium

(5386) tethraterinntothol = E100(#^^#)^#^#^####100

alternatively (5387) tethrathoth-ad-terinngathorium

(5388) tethrapentaeltothol = E100(#^^#)^#^#^#^#5

alternatively (5389) tethrathoth-ad-pentaelgathorium

( formally tethrapehaeltothol )

(5390) tethrahexaeltothol = E100(#^^#)^#^#^#^#6

alternatively (5391) tethrathoth-ad-hexaelgathorium

(5392) tethraheptaeltothol = E100(#^^#)^#^#^#^#7

alternatively (5393) tethrathoth-ad-heptaelgathorium

(5394) tethra-octaeltothol = E100(#^^#)^#^#^#^#8

alternatively (5395) tethrathoth-ad-octaelgathorium

(5396) tethra-ennaeltothol = E100(#^^#)^#^#^#^#9

alternatively (5397) tethrathoth-ad-ennaelgathorium

(5398) tethra-dekaeltothol = E100(#^^#)^#^#^#^#10

alternatively (5399) tethrathoth-ad-dekaelgathorium

...

(5400) tethragodtertol = E100(#^^#)^#^#^#^#100

alternatively (5401) tethrathoth-ad-godtotholium

( formally tethragodtertathol )

(5402) tethragodtopol = E100(#^^#)^(#^^#)5

alternatively (5403) tethrathoth-ad-godtertolium

( formally tethragodpeptathol )

(5404) tethragodhathor = E100(#^^#)^(#^^#)6

alternatively (5405) tethrathoth-ad-godtopolium

( formally tethragodextathol )

(5406) tethragodheptol = E100(#^^#)^(#^^#)7

alternatively (5407) tethrathoth-ad-godhathorium

( formally tethragodeptathol )

(5408) tethragodoctol = E100(#^^#)^(#^^#)8

alternatively (5409) tethrathoth-ad-godheptolium

( formally tethragodoctathol )

(5410) tethragodentol = E100(#^^#)^(#^^#)9

alternatively (5411) tethrathoth-ad-godoctolium

(5412) tethragoddekathol = E100(#^^#)^(#^^#)10

alternatively (5413) tethrathoth-ad-godentolium

We can go even further with...

(5414) tethragodendekathol = E100(#^^#)^(#^^#)11

alternatively (5415) tethrathoth-ad-goddekatholium

(5416) tethragoddodekathol = E100(#^^#)^(#^^#)12

alternatively (5417) tethrathoth-ad-godendekatholium

(5418) tethragodtriadekathol = E100(#^^#)^(#^^#)13

alternatively (5419) tethrathoth-ad-goddodekatholium

(5420) tethragodtetradekathol = E100(#^^#)^(#^^#)14

alternatively (5421) tethrathoth-ad-godtriadekatholium

(5422) tethragodpentadekathol = E100(#^^#)^(#^^#)15

alternatively (5423) tethrathoth-ad-godtetradekatholium

(5424) tethragodhexadekathol = E100(#^^#)^(#^^#)16

alternatively (5425) tethrathoth-ad-godpentadekatholium

(5426) tethragodheptadekathol = E100(#^^#)^(#^^#)17

alternatively (5427) tethrathoth-ad-godhexadekatholium

(5428) tethragodoctadekathol = E100(#^^#)^(#^^#)18

alternatively (5429) tethrathoth-ad-godheptadekatholium

(5430) tethragodennadekathol = E100(#^^#)^(#^^#)19

alternatively (5431) tethrathoth-ad-godoctadekatholium

(5432) tethragod-icosathol = E100(#^^#)^(#^^#)20

alternatively (5433) tethrathoth-ad-godennadekatholium

we can also have...

(5434) tethrathoth-ad-god-icosatholium = E100(#^^#)^(#^^#)21

...

(5435) tethragodtriantathol = E100(#^^#)^(#^^#)30

(5436) tethrathoth-ad-godtriantatholium = E100(#^^#)^(#^^#)31

(5437) tethragodsarantathol = E100(#^^#)^(#^^#)40

(5438) tethrathoth-ad-godsarantatholium = E100(#^^#)^(#^^#)41

(5439) tethragodpenintathol = E100(#^^#)^(#^^#)50

(5440) tethrathoth-ad-godpenintatholium = E100(#^^#)^(#^^#)51

(5441) tethragodexintathol = E100(#^^#)^(#^^#)60

(5442) tethrathoth-ad-godexintatholium = E100(#^^#)^(#^^#)61

(5443) tethragodebdomintathol = E100(#^^#)^(#^^#)70

(5444) tethrathoth-ad-godebdomintatholium = E100(#^^#)^(#^^#)71

(5445) tethragodogdontathol = E100(#^^#)^(#^^#)80

(5446) tethrathoth-ad-godogdontatholium = E100(#^^#)^(#^^#)81

(5447) tethragodenenintathol = E100(#^^#)^(#^^#)90

(5448) tethrathoth-ad-godenenintatholium = E100(#^^#)^(#^^#)91

...

(5449) tethra-tethrathoth = E100(#^^#)^(#^^#)100

alternatively (5450) tethrathoth-ad-tethrathothium

                Now to get even further along in the progression...

(5451) tethraduliath E100(#^^#)^(#^^#)100

(also (5452) tethrathoth-doppolux, and tethra-tethrathoth )

Our various naming conventions allow for far more names than we can practically list out. For example...

(5453) tethrathoth-ad-tethrathothium-by-hyperion = E100(#^^#)^(#^^#)*#100 

(5454) tethrathoth-ad-tethrathothium-by-godgahlah = E100(#^^#)^(#^^#)*#^#100

(5455) tethrathoth-ad-tethrathoth-by-godgathor = E100(#^^#)^(#^^#)*#^#^#100

(5456) tethrathoth-ad-tethrathothium-by-godtothol = E100(#^^#)^(#^^#)*#^#^#^#100

(5457) tethrathoth-ad-tethrathothium-by-tethrathoth = E100(#^^#)^(#^^#)*(#^^#)100

(5458) tethrathoth-ad-tethrathothium-by-tethrafact = E100(#^^#)^(#^^#)*(#^^#)^#100

(5459) tethrathoth-ad-tethrathothium-by-tethrathoth-ad-godgahlahium
= E100(#^^#)^(#^^#)*(#^^#)^#^#100

etc.

These examples combine both the "ad" operator, which allows us to describe hyperion-exponentation, and the "by" operator which allows us to describe hyperion-multiplication. The "carta" operator can be thought of as describing hyperion-addition. Furthermore we may use the "power-modifiers" to get various powers of hyperion expressions. For example...

(5460) deutero-tethrathoth-ad-tethrathothium 
= E100(#^^#)^(#^^#)*(#^^#)^(#^^#)100

(5461) trito-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)3

(5462) teterto-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)4

(5463) pepto-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)5

(5464) exto-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)6

(5465) epto-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)7

(5466) ogdo-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)8

(5467) ento-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)9

(5468) dekato-tethrathoth-ad-tethrathothium
= E100(#^^#)^(#^^#*#)10

...

onto a faster diagonalization...

(5469) tethradulifact = E100(#^^#)^(#^^#*#)100

alternatively (5470) tethrathoth-ad-tethrathothiumfact

(5471) grideutertethraduliath = E100(#^^#)^(#^^#*##)100

alternatively (5472) tethrathoth-ad-tethrathothiumgrid

(5473) kubicutethraduliath = E100(#^^#)^(#^^#*###)100

alternatively (5474) tethrathoth-ad-tethrathothiumcube

(5475) quarticutethraduliath = E100(#^^#)^(#^^#*####)100

alternatively (5476) tethrathoth-ad-tethrathothiumtess

(5477) quinticutethraduliath = E100(#^^#)^(#^^#*#^#)5

alternatively (5478) tethrathoth-ad-tethrathothiumpent

(5479) sexticutethraduliath = E100(#^^#)^(#^^#*#^#)6

alternatively (5480) tethrathoth-ad-tethrathothiumhex

(5481) septicutethraduliath = E100(#^^#)^(#^^#*#^#)7

alternatively (5482) tethrathoth-ad-tethrathothiumhept

(5483) octicutethraduliath = E100(#^^#)^(#^^#*#^#)8

alternatively (5484) tethrathoth-ad-tethrathothiumogd

(5485) nonicutethraduliath = E100(#^^#)^(#^^#*#^#)9

alternatively (5486) tethrathoth-ad-tethrathothiumenn

(5487) decicutethraduliath = E100(#^^#)^(#^^#*#^#)10

alternatively (5488) tethrathoth-ad-tethrathothiumdeck

...

(5489) tethraduli-godgathor = E100(#^^#)^(#^^#*#^#)100

alternatively (5490) tethrathoth-ad-tethrathoth-by-godgahlahium

(5491) tethraduli-gralgathor = E100(#^^#)^(#^^#*#^##)100

alternatively (5492) tethrathoth-ad-tethrathoth-by-gridgahlahium

(5493) tethraduli-thraelgathor = E100(#^^#)^(#^^#*#^###)100

alternatively (5494) tethrathoth-ad-tethrathoth-by-kubikahlahium

(5495) tethraduli-terinngathor = E100(#^^#)^(#^^#*#^####)100

alternatively (5496) tethrathoth-ad-tethrathoth-by-quarticahlahium

(5497) tethraduli-pentaelgathor = E100(#^^#)^(#^^#*#^#^#)5

alternatively (5498) tethrathoth-ad-tethrathoth-by-quinticahlahium

(5499) tethraduli-hexaelgathor = E100(#^^#)^(#^^#*#^#^#)6

alternatively (5500) tethrathoth-ad-tethrathoth-by-sexticahlahium

(5501) tethraduli-heptaelgathor = E100(#^^#)^(#^^#*#^#^#)7

alternatively (5502) tethrathoth-ad-tethrathoth-by-septicahlahium

(5503) tethraduli-octaelgathor = E100(#^^#)^(#^^#*#^#^#)8

alternatively (5504) tethrathoth-ad-tethrathoth-by-octicahlahium

(5505) tethraduli-ennaelgathor = E100(#^^#)^(#^^#*#^#^#)9

alternatively (5506) tethrathoth-ad-tethrathoth-by-nonicahlahium

(5507) tethraduli-dekaelgathor = E100(#^^#)^(#^^#*#^#^#)10

alternatively (5508) tethrathoth-ad-tethrathoth-by-decicahlahium

...

(5509) tethraduli-godtothol = E100(#^^#)^(#^^#*#^#^#)100

alternatively (5510) tethrathoth-ad-tethrathoth-by-godgathorium

(5511) tethraduli-godtertol = E100(#^^#)^(#^^#*#^#^#^#)100

alternatively (5512) tethrathoth-ad-tethrathoth-by-godtotholium

(5513) tethraduli-godtopol = E100(#^^#)^(#^^#*#^^#)5

alternatively (5514) tethrathoth-ad-tethrathoth-by-godtertolium

(5515) tethraduli-godhathor = E100(#^^#)^(#^^#*#^^#)6

alternatively (5516) tethrathoth-ad-tethrathoth-by-godtopolium

(5517) tethraduli-godheptol = E100(#^^#)^(#^^#*#^^#)7

alternatively (5518) tethrathoth-ad-tethrathoth-by-godhathorium

(5519) tethraduli-godoctol = E100(#^^#)^(#^^#*#^^#)8

alternatively (5520) tethrathoth-ad-tethrathoth-by-godheptolium

(5521) tethraduli-godentol = E100(#^^#)^(#^^#*#^^#)9

alternatively (5522) tethrathoth-ad-tethrathoth-by-godoctolium

(5523) tethraduli-goddekathol = E100(#^^#)^(#^^#*#^^#)10

alternatively (5524) tethrathoth-ad-tethrathoth-by-godentolium

also...

(5525) tethrathoth-ad-tethrathoth-by-goddekatholium = E100(#^^#)^(#^^#*#^^#)11

...

(5526) tethraduli-god-icosathol = E100(#^^#)^(#^^#*#^^#)20

(5527) tethrathoth-ad-tethrathoth-by-god-icosatholium = E100(#^^#)^(#^^#*#^^#)21

(5528) tethraduli-godtriantathol = E100(#^^#)^(#^^#*#^^#)30

(5529) tethrathoth-ad-tethrathoth-by-godtriantatholium = E100(#^^#)^(#^^#*#^^#)31

(5530) tethraduli-godsarantathol = E100(#^^#)^(#^^#*#^^#)40

(5531) tethrathoth-ad-tethrathoth-by-godsarantatholium = E100(#^^#)^(#^^#*#^^#)41

(5532) tethraduli-godpenintathol = E100(#^^#)^(#^^#*#^^#)50

(5533) tethrathoth-ad-tethrathoth-by-godpenintatholium = E100(#^^#)^(#^^#*#^^#)51

(5534) tethraduli-godexintathol = E100(#^^#)^(#^^#*#^^#)60

(5535) tethrathoth-ad-tethrathoth-by-godexintatholium = E100(#^^#)^(#^^#*#^^#)61

(5536) tethraduli-godebdomintathol = E100(#^^#)^(#^^#*#^^#)70

(5537) tethrathoth-ad-tethrathoth-by-godebdomintatholium 
= E100(#^^#)^(#^^#*#^^#)71

(5538) tethraduli-godogdontathol = E100(#^^#)^(#^^#*#^^#)80

(5539) tethrathoth-ad-tethrathoth-by-godogdontatholium 
= E100(#^^#)^(#^^#*#^^#)81

(5540) tethraduli-godenenintathol = E100(#^^#)^(#^^#*#^^#)90

(5541) tethrathoth-ad-tethrathoth-by-godenenintatholium 
= E100(#^^#)^(#^^#*#^^#)91

...

(5542) tethrathruliath = E100(#^^#)^(#^^#*#^^#)100

alternatively (5543) tethrathoth-ad-deutero-tethrathothium

(5544) tethrathrulifact = E100(#^^#)^(#^^#*#^^#*#)100

(5545) grideutertethrathruliath = E100(#^^#)^(#^^#*#^^#*##)100

(5546) kubicutethrathruliath = E100(#^^#)^(#^^#*#^^#*###)100

(5547) quarticutethrathruliath = E100(#^^#)^(#^^#*#^^#*####)100

(5548) quinticutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)5

(5549) sexticutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)6

(5550) septicutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)7

(5551) octicutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)8

(5552) nonicutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)9

(5553) decicutethrathruliath = E100(#^^#)^(#^^#*#^^#*#^#)10

...

(5554) tethrathruli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#)2

(5555) tethrathruli-godtothol = E100(#^^#)^(#^^#*#^^#*#^^#)3

(5556) tethrathruli-godtertol = E100(#^^#)^(#^^#*#^^#*#^^#)4

(5557) tethrathruli-godtopol = E100(#^^#)^(#^^#*#^^#*#^^#)5

(5558) tethrathruli-godhathor E100(#^^#)^(#^^#*#^^#*#^^#)6

(5559) tethrathruli-godheptol E100(#^^#)^(#^^#*#^^#*#^^#)7

(5560) tethrathruli-godoctol E100(#^^#)^(#^^#*#^^#*#^^#)8

(5561) tethrathruli-godentol = E100(#^^#)^(#^^#*#^^#*#^^#)9

(5562) tethrathruli-goddekathol = E100(#^^#)^(#^^#*#^^#*#^^#)10

...

(5563) tethraterliath E100(#^^#)^(#^^#*#^^#*#^^#)100

alternatively (5564) tethrathoth-ad-trito-tethrathothium

(5565) tethraterlifact = E100(#^^#)^(#^^#*#^^#*#^^#*#)100

(5566) grideutertethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*##)100

(5567) kubicutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*###)100

(5568) quarticutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*####)100

(5569) quinticutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)5

(5570) sexticutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)6

(5571) septicutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)7

(5572) octicutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)8

(5573) nonicutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)9

(5574) decicutethraterliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^#)10

...

(5575) tethraterli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#)2

...

(5576) tethrapepliath = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#)100

alternatively (5577) tethrathoth-ad-teterto-tethrathothium

(5578) tethrapeplifact = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#)100

( also (5579) tethrapeplichain )

...

(5580) tethrapepli-godgathor = E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#)2

...

(5581) tethra-exliath = E100(#^^#)^(#^^#)^#5

alternatively (5582) tethrathoth-ad-pepto-tethrathothium

(5583) tethra-epliath = E100(#^^#)^(#^^#)^#6

alternatively (5584) tethrathoth-ad-exto-tethrathothium

(5585) tethra-ocliath = E100(#^^#)^(#^^#)^#7

alternatively (5586) tethrathoth-ad-epto-tethrathothium

(5587) tethra-enliath = E100(#^^#)^(#^^#)^#8

alternatively (5588) tethrathoth-ad-ogdo-tethrathothium

(5589) tethra-dekliath = E100(#^^#)^(#^^#)^#9

alternatively (5590) tethrathoth-ad-ento-tethrathothium

also...

(5591) tethrathoth-ad-dekato-tethrathothium = E100(#^^#)^(#^^#)^#10
...

(5592) tethra-icosaliath = E100(#^^#)^(#^^#)^#19

(5593) tethrathoth-ad-isosto-tethrathothium = E100(#^^#)^(#^^#)^#20

(5594) tethra-triantaliath = E100(#^^#)^(#^^#)^#29

(5595) tethrathoth-ad-trianto-tethrathothium = E100(#^^#)^(#^^#)^#30

(5596) tethra-sarantaliath = E100(#^^#)^(#^^#)^#39

(5597) tethrathoth-ad-saranto-tethrathothium = E100(#^^#)^(#^^#)^#40

(5598) tethra-penintaliath = E100(#^^#)^(#^^#)^#49

(5599) tethrathoth-ad-peninto-tethrathothium = E100(#^^#)^(#^^#)^#50 

(5600) tethra-exintaliath = E100(#^^#)^(#^^#)^#59

(5601) tethrathoth-ad-exinto-tethrathothium = E100(#^^#)^(#^^#)^#60

(5602) tethra-ebdomintaliath = E100(#^^#)^(#^^#)^#69

(5603) tethrathoth-ad-ebdominto-tethrathothium = E100(#^^#)^(#^^#)^#70

(5604) tethra-ogdontaliath = E100(#^^#)^(#^^#)^#79

(5605) tethrathoth-ad-ogdonto-tethrathothium = E100(#^^#)^(#^^#)^#80

(5606) tethra-enenintaliath = E100(#^^#)^(#^^#)^#89

(5607) tethrathoth-ad-eneninto-tethrathothium = E100(#^^#)^(#^^#)^#90

...




Monster-Giant Regiment

Category 59
Members: 277
(5608 - 5884)


φ(1,0)^φ(1,0)^ω



Here we reach the somewhat irregular Monster-Giant ...

(5608) Monster-Giant = E100(#^^#)^(#^^#)^#100 = 

E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*
#^^#*#^^#*#^^#*#^^#*#^^#*#^^#)100

What could be better than that? ...

(5609) grand Monster-Giant = E100(#^^#)^(#^^#)^#100#2 =

E100(#^^#)^(#^^#)^#[Monster-Giant]100 =

E100(#^^#)^(#^^#*#^^#*#^^#*#^^#* ... ... ... ... #^^#*#^^#*#^^#*#^^#)100

w/Monster-Giant #^^#s in the exponent

What's even better than that?! ...

(5610) Monster-Gigantri = E100(#^^#)^(#^^#)^#100(#^^#)^(#^^#)^#100

(5611) Monster-Gigantet = E100(#^^#)^(#^^#)^#*#4

(5612) Monster-Giganpent E100(#^^#)^(#^^#)^#*#5

(5613) Monster-Gigantex E100(#^^#)^(#^^#)^#*#6

(5614) Monster-Gigantep E100(#^^#)^(#^^#)^#*#7

(5615) Monster-Gigantoch E100(#^^#)^(#^^#)^#*#8

(5616) Monster-Giganenn = E100(#^^#)^(#^^#)^#*#9

(5617) Monster-Gigandek = E100(#^^#)^(#^^#)^#*#10

what's even better than that?!? ...

(5618) deutero-Monster-Giant = E100(#^^#)^(#^^#)^#*(#^^#)^(#^^#)^#100

(5619) trito-Monster-Giant = E100(#^^#)^((#^^#)^#*#)3

(5620) teterto-Monster-Giant = E100(#^^#)^((#^^#)^#*#)4

(5621) pepto-Monster-Giant = E100(#^^#)^((#^^#)^#*#)5

(5622) exto-Monster-Giant = E100(#^^#)^((#^^#)^#*#)6

(5623) epto-Monster-Giant = E100(#^^#)^((#^^#)^#*#)7

(5624) ogdo-Monster-Giant = E100(#^^#)^((#^^#)^#*#)8

(5625) ento-Monster-Giant = E100(#^^#)^((#^^#)^#*#)9

(5626) dekato-Monster-Giant = E100(#^^#)^((#^^#)^#*#)10

...

(5627) hecato-Monster-Giant = E100(#^^#)^((#^^#)^#*#)100


                Here things get kinda complicated ...

E100(#^^#)^((#^^#)^#*#^^#)100

Note that this number IS NOT E100(#^^#)^(#^^#)^#101. This number is much much smaller than E100(#^^#)^((#^^#)^#*#^^#)100. Remember that only the last #^^# get's decomposed. Only once this completely decays do we get to decompose (#^^#)^#. At this point however "n", the last argument, is so unfathomably large, that comparison with the Monster-Giant is absurdly insulting... and we are just getting started with xE^ ...

(5628) tethra-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#)100

(5629) tethraduli-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#*#^^#)100

(5630) tethrathruli-Monster-Giant = E100(#^^#)^((#^^#)^#*#^^#*#^^#*#^^#)100

(5631) tethraterli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)4

(5632) tethrapepli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)5

(5633) tethraexli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)6

(5634) tethraepli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)7

(5635) tethraocli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)8

(5636) tethra-enli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)9

(5637) tethradekli-Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)10

...

(5638) Monster Monster-Giant = E100(#^^#)^((#^^#)^#*(#^^#)^#)100

alternatively ...

 (5639) two-ex-Monster-Giant = E100(#^^#)^(#^^#)^##2

This allows us to continue with ...

(5640) three-ex-Monster-Giant = E100(#^^#)^(#^^#)^##3

(5641) four-ex-Monster-Giant = E100(#^^#)^(#^^#)^##4

(5642) five-ex-Monster-Giant = E100(#^^#)^(#^^#)^##5

(5643) six-ex-Monster-Giant = E100(#^^#)^(#^^#)^##6

(5644) seven-ex-Monster-Giant = E100(#^^#)^(#^^#)^##7

(5645) eight-ex-Monster-Giant = E100(#^^#)^(#^^#)^##8

(5646) nine-ex-Monster-Giant = E100(#^^#)^(#^^#)^##9

(5647) ten-ex-Monster-Giant = E100(#^^#)^(#^^#)^##10

...

(5648) hundred-ex-Monster-Giant = E100(#^^#)^(#^^#)^##100

(5649) Monster-Giant-ex-Monster-Giant = E100(#^^#)^(#^^#)^##Monster-Giant

(5650) grand hundred-ex-Monster-Giant = E100(#^^#)^(#^^#)^##100#2 =

E100(#^^#)^(#^^#)^##hundred-ex-Monster-Giant

                With that exhausted we need something new ...

(5651) Monster-Grid = E100(#^^#)^(#^^#)^##100

This is another name for hundred-ex-Monster-Giant, but it allows us to continue with ...

(5652) Monster-Cube = E100(#^^#)^(#^^#)^###100

(5653) Monster-Tesseract = E100(#^^#)^(#^^#)^####100

(5654) Monster-Penteract = E100(#^^#)^(#^^#)^(#^5)100

(5655) Monster-Hexeract = E100(#^^#)^(#^^#)^(#^6)100

(5656) Monster-Hepteract = E100(#^^#)^(#^^#)^(#^7)100

(5657) Monster-Octeract = E100(#^^#)^(#^^#)^(#^8)100

(5658) Monster-Enneract = E100(#^^#)^(#^^#)^(#^9)100

(5659) Monster-Dekeract = E100(#^^#)^(#^^#)^(#^10)100
 
...
 
 (5660) Monster-Hecateract = E100(#^^#)^(#^^#)^#^#100 =
 
          E100(#^^#)^(#^^#)^####################
####################
####################
####################
                                             ####################100

That's pretty cool. But we can go much further using the "ad" operator along with the names we previously established in the tethrathoth regiment. For example...

(5661) tethrathoth-ad-tethrathoth-ad-gridgahlahiumium 
= E100(#^^#)^(#^^#)^#^##100

(5662) tethrathoth-ad-tethrathoth-ad-kubikahlahiumium 
= E100(#^^#)^(#^^#)^#^###100

(5663) tethrathoth-ad-tethrathoth-ad-quarticahlahiumium 
= E100(#^^#)^(#^^#)^#^####100

(5664) tethrathoth-ad-tethrathoth-ad-quinticahlahiumium
= E100(#^^#)^(#^^#)^#^#^#5

(5665) tethrathoth-ad-tethrathoth-ad-sexticahlahiumium
= E100(#^^#)^(#^^#)^#^#^#6

(5666) tethrathoth-ad-tethrathoth-ad-septicahlahiumium
= E100(#^^#)^(#^^#)^#^#^#7

(5667) tethrathoth-ad-tethrathoth-ad-octicahlahiumium
= E100(#^^#)^(#^^#)^#^#^#8

(5668) tethrathoth-ad-tethrathoth-ad-nonicahlahiumium
= E100(#^^#)^(#^^#)^#^#^#9

(5669) tethrathoth-ad-tethrathoth-ad-decicahlahiumium
= E100(#^^#)^(#^^#)^#^#^#10

...

(5670) tethrathoth-ad-tethrathoth-ad-godgathoriumium
= E100(#^^#)^(#^^#)^#^#^#100

(5671) tethrathoth-ad-tethrathoth-ad-godtotholiumium
= E100(#^^#)^(#^^#)^#^#^#^#100

(5672) tethrathoth-ad-tethrathoth-ad-godtertoliumium
= E100(#^^#)^(#^^#)^#^^#5

(5673) tethrathoth-ad-tethrathoth-ad-godtopoliumium
= E100(#^^#)^(#^^#)^#^^#6

(5674) tethrathoth-ad-tethrathoth-ad-godhathoriumium
= E100(#^^#)^(#^^#)^#^^#7

(5675) tethrathoth-ad-tethrathoth-ad-godheptoliumium
= E100(#^^#)^(#^^#)^#^^#8

(5676) tethrathoth-ad-tethrathoth-ad-godoctoliumium
= E100(#^^#)^(#^^#)^#^^#9

(5677) tethrathoth-ad-tethrathoth-ad-godentoliumium
= E100(#^^#)^(#^^#)^#^^#10

(5678) tethrathoth-ad-tethrathoth-ad-goddekatholiumium
= E100(#^^#)^(#^^#)^#^^#11

...

(5679) tethrathoth-ad-tethraduliathium = E100(#^^#)^(#^^#)^(#^^#)100

(5680) tethrathoth-ad-tethraduliathium-by-tethrathoth 
= E100(#^^#)^(#^^#)^(#^^#)*#^^#100

(5681) tethrathoth-ad-tethraduliath-by-tethrathothium
= E100(#^^#)^((#^^#)^(#^^#)*#^^#)100

... yup ... we have to go through all the lower levels with #^^# to get back to the top of the stack of #^^#s. After a considerably laborious climb we would eventually reach...

(5682) tethrathoth-ad-tethrathruliathium 
= E100(#^^#)^(#^^#)^(#^^#*#^^#)100

...and then...

(5683) tethrathoth-ad-tethraterliathium
= E100(#^^#)^(#^^#)^(#^^#*#^^#*#^^#)100

(5684) tethrathoth-ad-tethrapepliathium
= E100(#^^#)^(#^^#)^(#^^#*#^^#*#^^#*#^^#)100

(5685) tethrathoth-ad-tethra-exliathium
= E100(#^^#)^(#^^#)^(#^^#)^#5

(5686) tethrathoth-ad-tethra-epliathium
= E100(#^^#)^(#^^#)^(#^^#)^#6

(5687) tethrathoth-ad-tethra-ocliathium
= E100(#^^#)^(#^^#)^(#^^#)^#7

(5688) tethrathoth-ad-tethra-enliathium
= E100(#^^#)^(#^^#)^(#^^#)^#8

(5689) tethrathoth-ad-tethra-dekliathium
= E100(#^^#)^(#^^#)^(#^^#)^#9

...
 
    Diagonalizing on a larger scale we can say...
 
(5690) Super Monster-Giant = E100(#^^#)^(#^^#)^(#^^#)^#100
 
(5691) Super Monster-Grid = E100(#^^#)^(#^^#)^(#^^#)^##100
 
(5692) Super Monster-Cube = E100(#^^#)^(#^^#)^(#^^#)^###100
 
(5693) Super Monster-Tesseract = E100(#^^#)^(#^^#)^(#^^#)^####100

(5694) Super Monster-Penteract = E100(#^^#)^(#^^#)^(#^^#)^(#^5)100

(5695) Super Monster-Hexeract = E100(#^^#)^(#^^#)^(#^^#)^(#^6)100

(5696) Super Monster-Hepteract = E100(#^^#)^(#^^#)^(#^^#)^(#^7)100

(5697) Super Monster-Octeract = E100(#^^#)^(#^^#)^(#^^#)^(#^8)100

(5698) Super Monster-Enneract = E100(#^^#)^(#^^#)^(#^^#)^(#^9)100

(5699) Super Monster-Dekeract = E100(#^^#)^(#^^#)^(#^^#)^(#^10)100 
 
...
 
(5700) Super Monster-Hecateract = E100(#^^#)^(#^^#)^(#^^#)^#^#100
 
...
 
(5701) Double-Super Monster-Giant = E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100
 
(5702) Triple-Super Monster-Giant 
= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5703) Quadruple-Super Monster-Giant
= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5704) Quintuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5705) Sextuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5706) Septuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^
(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5707) Octuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^
^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5708) Nonuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^
(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5709) Decuple-Super Monster-Giant

= E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^
(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)^#100
 
...
 
Here an alternative diagonalization series. It has the advantage of having a more compact form since it occurs along a standard fundamental sequence ...
 
(5710) tethrathoth-dubletetrate = E100(#^^#)^(#^^#)100

This is equivalent to tethraduliath ( See Member No.5451 ), but this form allow us to continue with ...
 
(5711) tethrathoth-trebletetrate = E100(#^^#)^(#^^#)^(#^^#)100
 
(5712) tethrathoth-quadrupletetrate = E100(#^^#)^(#^^#)^(#^^#)^(#^^#)100
 
(5713) tethrathoth-quintupletetrate = E100(#^^#)^^#5
 
(5714) tethrathoth-sextupletetrate = E100(#^^#)^^#6
 
(5715) tethrathoth-septupletetrate = E100(#^^#)^^#7
 
(5716) tethrathoth-octupletetrate = E100(#^^#)^^#8 

(5717) tethrathoth-nonupletetrate = E100(#^^#)^^#9

(5718) tethrathoth-decupletetrate = E100(#^^#)^^#10
 
...

Finally we arrive at...
 
(5719) terrible tethrathoth = E100(#^^#)^^#100 =
 
E100(#^^#)^(#^^#)^(#^^#)^ ... ... ^(#^^#)^(#^^#)^(#^^#)100 w/100 #^^#s

(5720) terrified-tethrathoth-by-hyperion = E100(#^^#*#)^^#100

This number is a rogue type formed by applying the "terrible"-operator after all the other operators. What is interesting is that (#^^#*#)^^# diagonalizes over the same set of delimiters that (#^^#)^^# diagonalizes over, and thus (#^^#*#)^^# does not grow faster than (#^^#)^^#. Thus, although this number must necessarily be bigger than terrible tethrathoth since it expands out to E100(#^^#*#)^(#^^#*#)^(#^^#*#)^...^(#^^#*#)100 w/100 (#^^#*#)s. It is in some sense not a significant difference. This is true even if we use larger arguments. such as...

(5721) terrified-deutero-tethrathoth = E100(#^^#*#^^#)^^#100

or even more exotic like...

(5722) terrified-tethrafact = E100((#^^#)^#)^^#100

(5723) terrified-tethraduliath = E100((#^^#)^#^^#)^^#100

(5724) terrified-Monster-Giant = E100((#^^#)^(#^^#)^#)^^#100

(5725) terrified-Super-Monster-Giant = E100((#^^#)^(#^^#)^(#^^#)^#)^^#100

in fact even if we go so far as to have...

(5726) terrified-terrible-tethrathoth = E100((#^^#)^^100)^^#100

this is STILL tiny in comparison to...

(5727) grand terrible tethrathoth = E100(#^^#)^^#100#2 

= E100(#^^#)^^#(terrible tethrathoth)

= E100(#^^#)^(#^^#)^(#^^#)^ ... ... ... ... ^(#^^#)^(#^^#)^(#^^#)100

w/terrible tethrathoth #^^#s

o_0;

We can use any delimiter, say '&', below (#^^#)^^# in fact, and always get a function which is no more than an offset of E100(#^^#)^^#n. That is...

E100&^^#n ~ E100(#^^#)^^#(n+k)

with some offset "k" assuming & < (#^^#)^^#. Yet the moment & = (#^^#)^^# we get a radically different growth rate! Strange.

In any case we can now move on to...

(5728) grangol-carta-terrible tethrathoth = E100(#^^#)^^#100#100

(5729) godgahlah-carta-terrible tethrathoth = E100(#^^#)^^#100#^#100

(5730) tethrathoth-carta-terrible tethrathoth = E100(#^^#)^^#100#^^#100

(5731) Monster-Giant-carta-terrible tethrathoth 

= E100(#^^#)^^#100(#^^#)^(#^^#)^#100

...

(5732) territritethrathoth = E100(#^^#)^^#100(#^^#)^^#100

(5733) territertethrathoth = E100(#^^#)^^#100(#^^#)^^#100(#^^#)^^#100

(5734) terripetethrathoth = E100(#^^#)^^#*#5

(5735) terri-extethrathoth = E100(#^^#)^^#*#6

(5736) terri-eptethrathoth = E100(#^^#)^^#*#7

(5737) terri-octethrathoth = E100(#^^#)^^#*#8

(5738) terri-entethrathoth = E100(#^^#)^^#*#9

(5739) terri-dektethrathoth = E100(#^^#)^^#*#10

...

diagonalizing on a higher level we have...

(5740) terrible-tethrathoth-by-hyperion = E100(#^^#)^^#*#100

(5741) terrible-tethrathoth-by-deutero-hyperion = E100(#^^#)^^#*##100

(5742) terrible-tethrathoth-by-trito-hyperion = E100(#^^#)^^#*###100

(5743) terrible-tethrathoth-by-teterto-hyperion = E100(#^^#)^^#*####100

(5744) terrible-tethrathoth-by-godgahlah = E100(#^^#)^^#*#^#100

(5745) terrible-tethrathoth-by-deutero-godgahlah = E100(#^^#)^^#*#^#*#^#100

(5746) terrible-tethrathoth-by-gridgahlah = E100(#^^#)^^#*#^##100

(5747) terrible-tethrathoth-by-kubikahlah = E100(#^^#)^^#*#^###100

(5748) terrible-tethrathoth-by-quarticahlah = E100(#^^#)^^#*#^####100

(5749) terrible-tethrathoth-by-godgathor = E100(#^^#)^^#*#^#^#100

(5750) terrible-tethrathoth-by-godtothol = E100(#^^#)^^#*#^#^#^#100

(5751) terrible-tethrathoth-by-godtertol = E100(#^^#)^^#*#^^#5

(5752) terrible-tethrathoth-by-godtopol = E100(#^^#)^^#*#^^#6

(5753) terrible-tethrathoth-by-godhathor = E100(#^^#)^^#*#^^#7

(5754) terrible-tethrathoth-by-godheptol = E100(#^^#)^^#*#^^#8

(5755) terrible-tethrathoth-by-godoctol = E100(#^^#)^^#*#^^#9

(5756) terrible-tethrathoth-by-godentol = E100(#^^#)^^#*#^^#10

(5757) terrible-tethrathoth-by-goddekathol = E100(#^^#)^^#*#^^#11

...

(5758) terrible-tethrathoth-by-tethrathoth = E100(#^^#)^^#*#^^#100

(5759) terrible-tethrathoth-by-deutero-tethrathoth = E100(#^^#)^^#*#^^#*#^^#100

(5760) terrible-tethrathoth-by-tethrafact = E100(#^^#)^^#*(#^^#)^#100

(5761) terrible-tethrathoth-by-tethrathoth-dubletetrate 
= E100(#^^#)^^#*(#^^#)^(#^^#)100

(5762) terrible-tethrathoth-by-Monster-Giant
= E100(#^^#)^^#*(#^^#)^(#^^#)^#100

(5763) terrible-tethrathoth-by-tethrathoth-trebletetrate
= E100(#^^#)^^#*(#^^#)^(#^^#)^(#^^#)100

(5764) terrible-tethrathoth-by-Super-Monster-Giant
= E100(#^^#)^^#*(#^^#)^(#^^#)^(#^^#)^#100

(5765) terrible-tethrathoth-by-tethrathoth-quadrupletetrate 
= E100(#^^#)^^#*(#^^#)^(#^^#)^(#^^#)^(#^^#)100

(5766) terrible-tethrathoth-by-tethrathoth-quintupletetrate
= E100(#^^#)^^#*(#^^#)^^#5

(5767) terrible-tethrathoth-by-tethrathoth-sextupletetrate
= E100(#^^#)^^#*(#^^#)^^#6

(5768) terrible-tethrathoth-by-tethrathoth-septupletetrate
= E100(#^^#)^^#*(#^^#)^^#7

(5769) terrible-tethrathoth-by-tethrathoth-octupletetrate
= E100(#^^#)^^#*(#^^#)^^#8

(5770) terrible-tethrathoth-by-tethrathoth-nonupletetrate
= E100(#^^#)^^#*(#^^#)^^#9

(5771) terrible-tethrathoth-by-tethrathoth-decupletetrate
= E100(#^^#)^^#*(#^^#)^^#10

...

(5772) deutero-terrible-tethrathoth = E100(#^^#)^^#*(#^^#)^^#100

(5773) trito-terrible-tethrathoth 
= E100(#^^#)^^#*(#^^#)^^#*(#^^#)^^#100

(5774) teterto-terrible-tethrathoth 
= E100(#^^#)^^#*(#^^#)^^#*(#^^#)^^#*(#^^#)^^#100
= E100((#^^#)^^#)^#4

(5775) pepto-terrible-tethrathoth = E100((#^^#)^^#)^#5

(5776) exto-terrible-tethrathoth = E100((#^^#)^^#)^#6

(5777) epto-terrible-tethrathoth = E100((#^^#)^^#)^#7

(5778) ogdo-terrible-tethrathoth = E100((#^^#)^^#)^#8

(5779) ento-terrible-tethrathoth = E100((#^^#)^^#)^#9

(5780) dekato-terrible-tethrathoth = E100((#^^#)^^#)^#10

...

(5781) hecato-terrible-tethrathoth = E100((#^^#)^^#)^#100

(5782) hecato-hecato-terrible-tethrathoth = E100((#^^#)^^#)^##100

alternatively (5783) territethrathothigrid

(5784) hecato-hecato-hecato-terrible-tethrathoth = E100((#^^#)^^#)^###100

alternatively (5785) territethrathothicube

(5786) hecato-hecato-hecato-hecato-terrible-tethrathoth = E100((#^^#)^^#)^####100

alternatively (5787) territethrathothitess

...

(5788) terrible-tethrathoth-ipso-godgahlah = E100((#^^#)^^#)^#^#100

alternatively (5789) territethrathoth-ad-godgahlahium

(5790) terrible-tethrathoth-ipso-gridgahlah = E100((#^^#)^^#)^#^##100

(5791) terrible-tethrathoth-ipso-kubikahlah = E100((#^^#)^^#)^#^###100

(5792) terrible-tethrathoth-ipso-quarticahlah = E100((#^^#)^^#)^#^####100

...

(5793) terrible-tethrathoth-ipso-godgathor = E100((#^^#)^^#)^#^#^#100

alternatively (5794) territethrathoth-ad-godgathorium

(5795) terrible-tethrathoth-ipso-godtothol = E100((#^^#)^^#)^#^#^#^#100

alternatively (5796) territethrathoth-ad-godtotholium

(5797) terrible-tethrathoth-ipso-godtertol = E100((#^^#)^^#)^#^^#5

alternatively (5798) territethrathoth-ad-godtertolium

(5799) terrible-tethrathoth-ipso-godtopol = E100((#^^#)^^#)^#^^#6

alternatively (5800) territethrathoth-ad-godtopolium

(5801) terrible-tethrathoth-ipso-godhathor = E100((#^^#)^^#)^#^^#7

alternatively (5802) territethrathoth-ad-godhathorium

(5803) terrible-tethrathoth-ipso-godheptol = E100((#^^#)^^#)^#^^#8

alternatively (5804) territethrathoth-ad-godheptolium

(5805) terrible-tethrathoth-ipso-godoctol = E100((#^^#)^^#)^#^^#9

alternatively (5806) territethrathoth-ad-godoctolium

(5807) terrible-tethrathoth-ipso-godentol = E100((#^^#)^^#)^#^^#10

alternatively (5808) territethrathoth-ad-godentolium

(5809) terrible-tethrathoth-ipso-goddekathol = E100((#^^#)^^#)^#^^#11

alternatively (5810) territethrathoth-ad-goddekatholium

...

(5811) terrible-tethrathoth-ipso-tethrathoth = E100((#^^#)^^#)^#^^#100

alternatively (5812) territethrathoth-ad-tethrathothium

(5813) terrible-tethrathoth-ipso-deutero-tethrathoth
= E100((#^^#)^^#)^(#^^#*#^^#)100

(5814) terrible-tethrathoth-ipso-trito-tethrathoth
= E100((#^^#)^^#)^(#^^#*#^^#*#^^#)100

(5815) terrible-tethrathoth-ipso-teterto-tethrathoth
= E100((#^^#)^^#)^(#^^#*#^^#*#^^#*#^^#)100

(5816) terrible-tethrathoth-ipso-pepto-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#5

(5817) terrible-tethrathoth-ipso-exto-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#6

(5818) terrible-tethrathoth-ipso-epto-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#7

(5819) terrible-tethrathoth-ipso-ogdo-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#8

(5820) terrible-tethrathoth-ipso-ento-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#9

(5821) terrible-tethrathoth-ipso-dekato-tethrathoth
= E100((#^^#)^^#)^(#^^#)^#10

...

(5822) terrible-tethrathoth-ipso-tethrafact = E100((#^^#)^^#)^(#^^#)^#100

(5823) terrible-tethrathoth-ipso-tethrathoth-ipso-tethrathoth 
= E100((#^^#)^^#)^(#^^#)^(#^^#)100

alternatively (5824) territethrathoth-ad-dubletetrated-tethrathothium

(5825) terrible-tethrathoth-ipso-Monster-Giant
= E100((#^^#)^^#)^(#^^#)^(#^^#)^#100

(5826) terrible-tethrathoth-ipso-tethrathoth-trebletetrate
= E100((#^^#)^^#)^(#^^#)^(#^^#)^(#^^#)100

alternatively (5827) territethrathoth-ad-trebletetrated-tethrathothium

(5828) terrible-tethrathoth-ipso-Super-Monster-Giant
= E100((#^^#)^^#)^(#^^#)^(#^^#)^(#^^#)^#100

(5829) terrible-tethrathoth-ipso-tethrathoth-quadrupletetrate
= E100((#^^#)^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#)100
= E100((#^^#)^^#)^(#^^#)^^#4

(5830) terrible-tethrathoth-ipso-tethrathoth-quintupletetrate
= E100((#^^#)^^#)^(#^^#)^^#5

(5831) terrible-tethrathoth-ipso-tethrathoth-sextupletetrate
= E100((#^^#)^^#)^(#^^#)^^#6

(5832) terrible-tethrathoth-ipso-tethrathoth-septupletetrate
= E100((#^^#)^^#)^(#^^#)^^#7

(5833) terrible-tethrathoth-ipso-tethrathoth-octupletetrate
= E100((#^^#)^^#)^(#^^#)^^#8

(5834) terrible-tethrathoth-ipso-tethrathoth-nonupletetrate
= E100((#^^#)^^#)^(#^^#)^^#9

(5835) terrible-tethrathoth-ipso-tethrathoth-decupletetrate
= E100((#^^#)^^#)^(#^^#)^^#10

...

(5836) dubletetrated terrible tethrathoth 
= E100((#^^#)^^#)^((#^^#)^^#)100

alternatively (5837) dubletetrated-territethrathoth
 
(5838) trebletetrated terrible tethrathoth = E100((#^^#)^^#)^((#^^#)^^#)^((#^^#)^^#)100

alternatively (5839) trebletetrated-territethrathoth
 
(5840) quadrupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#4

alternatively (5841) quadrupletetrated-territethrathoth
 
(5842) quintupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#5
 
(5843) sextupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#6
 
(5844) septupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#7
 
(5845) octupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#8

(5846) nonupletetrated terrible tethrathoth = E100((#^^#)^^#)^^#9

(5847) decupletetrated terrible tethrathoth = E100(#^^#)^^#)^^#10
 
...
 
(5848) terrible terrible tethrathoth = E100((#^^#)^^#)^^#100
 
(5849) dubletetrated terrible terrible tethrathoth = E100(((#^^#)^^#)^^#)^(((#^^#)^^#)^^#)100 
 
(5850) trebletetrated terrible terrible tethrathoth 
= E100(((#^^#)^^#)^^#)^^#3
 
(5851) quadrupletetrated terrible terrible tethrathoth 
= E100(((#^^#)^^#)^^#)^^#4

(5852) quintupletetrated terrible terrible tethrathoth 
= E100(((#^^#)^^#)^^#)^^#5

(5853) sextupletetrated terrible terrible tethrathoth
= E100(((#^^#)^^#)^^#)^^#6

(5854) septupletetrated terrible terrible tethrathoth
= E100(((#^^#)^^#)^^#)^^#7

(5855) octupletetrated terrible terrible tethrathoth
= E100(((#^^#)^^#)^^#)^^#8

(5856) nonupletetrated terrible terrible tethrathoth
= E100(((#^^#)^^#)^^#)^^#9

(5857) decupletetrated terrible terrible tethrathoth
= E100(((#^^#)^^#)^^#)^^#10
...
 
(5858) triple-terrible tethrathoth = E100(((#^^#)^^#)^^#)^^#100

alternatively (5859) terrible terrible terrible tethrathoth

(5860) dubletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#2

(5861) trebletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#3

(5862) quadrupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#4

(5863) quintupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#5

(5864) sextupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#6

(5865) septupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#7

(5866) octupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#8

(5867) nonupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#9

(5868) decupletetrated triple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#10

...

(5869) quadruple-terrible tethrathoth 
= E100((((#^^#)^^#)^^#)^^#)^^#100
= E100#^^#>#5

alternatively (5870) terrible terrible terrible terrible tethrathoth

(5871) quintuple-terrible tethrathoth = E100#^^#>#6

(5872) sextuple-terrible tethrathoth = E100#^^#>#7

(5873) septuple-terrible tethrathoth = E100#^^#>#8

(5874) octuple-terrible tethrathoth = E100#^^#>#9

(5875) nonuple-terrible tethrathoth = E100#^^#>#10

(5876) decuple-terrible tethrathoth = E100#^^#>#11
 
...

(5877) vigintuple-terrible tethrathoth = E100#^^#>#21

(5878) trigintuple-terrible tethrathoth = E100#^^#>#31

(5879) quadragintuple-terrible tethrathoth = E100#^^#>#41

(5880) quinquagintuple-terrible tethrathoth = E100#^^#>#51

(5881) sexagintuple-terrible tethrathoth = E100#^^#>#61

(5882) septuagintuple-terrible tethrathoth = E100#^^#>#71

(5883) octogintuple-terrible tethrathoth = E100#^^#>#81

(5884) nonagintuple-terrible tethrathoth = E100#^^#>#91

...


Tethriterator Regiment

Category 60
Members: 521
(5885 - 6405)


φ(1,ω)



                    ... at (5885) ninety-nine-ex-terrible tethrathoth we reach the tethrathoth ba'al. This is where I reached the end of LECEN previously and where the set of delimiters reached its breaking point. However we now have a complete system for continuing through all the hyper-operations. We simply use a carrot top to denote the number of applications of the '^^#' operator to '#'. I will also rechristen this number in order for it to be more extensible. Here is the new definition and name...
 
(5886) tethriterator = E100#^^#>#100

also called (5887) tethrathoth ba'al
 
This number is now called the tethriterator (tetration + iterator), since it's delimiter iterates the smallest tetrational operator, ^^#

                            Note that this number is also equivalent to ninety-nine-ex-terrible-tethrathoth. How far can we go with the -ex-terrible operator? In our previous work with Cascading-E Notation many numbers of this form were given. Now we have a compact way to write them...

(5888) hundred-ex-terrible tethrathoth = E100#^^#>#101

(5889) googol-ex-terrible tethrathoth = E100#^^#>#(1+E100)

 

(5890) grangol-ex-terrible tethrathoth = E100#^^#>#(1+E100#100)

 

(5891) greagol-ex-terrible tethrathoth = E100#^^#>#(1+E100##3)

 

(5892) gigangol-ex-terrible tethrathoth = E100#^^#>#(1+E100##4)


(5893) gorgegol-ex-terrible tethrathoth = E100#^^#>#(1+E100##5)


(5894) gulgol-ex-terrible tethrathoth = E100#^^#>#(1+E100##6)


(5895) gaspgol-ex-terrible tethrathoth = E100#^^#>#(1+E100##7)


(5896) ginorgol-ex-terrible tethrathoth = E100#^^#>#(1+E100##8)


(5897) gargantuul-ex-terrible tethrathoth = E100#^^#>#(1+E100##9)


(5898) googondol-ex-terrible tethrathoth = E100#^^#>#(1+E100##10)


(5899) gugold-ex-terrible tethrathoth = E100#^^#>#(1+E100##100)

 

(5900) gugolthra-ex-terrible tethrathoth = E100#^^#>#(1+E100###3)


(5901) gugoltesla-ex-terrible tethrathoth = E100#^^#>#(1+E100###4)


(5902) gugolpeta-ex-terrible tethrathoth = E100#^^#>#(1+E100###5)


(5903) gugolhexa-ex-terrible tethrathoth = E100#^^#>#(1+E100###6)


(5904) gugolhepta-ex-terrible tethrathoth = E100#^^#>#(1+E100###7)


(5905) gugolocta-ex-terrible tethrathoth = E100#^^#>#(1+E100###8)


(5906) gugolenna-ex-terrible tethrathoth = E100#^^#>#(1+E100###9)


(5907) gugoldeka-ex-terrible tethrathoth = E100#^^#>#(1+E100###10)

 

(5908) throogol-ex-terrible tethrathoth = E100#^^#>#(1+E100###100)

 

(5909) tetroogol-ex-terrible tethrathoth = E100#^^#>#(1+E100####100)


(5910) pentoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#5)


(5911) hexoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#6)


(5912) heptoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#7)


(5913) ogdoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#8)


(5914) entoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#9)


(5915) dektoogol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#10)

 

(5916) godgahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#100)

 

(5917) gridgahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^##100)

 

(5918) kubikahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^###100)

 

(5919) quarticahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^####100)

 

(5920) quinticahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#5)

 

(5921) sexticahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#6)

 

(5922) septicahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#7)

 

(5923) octicahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#8)


(5924) nonicahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#9)


(5925) decicahlah-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#10)

 

(5926) godgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#100)

 

(5927) goober bunch-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#101)

 

(5928) gralgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^##100)

 

(5929) thraelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^###100)

 

(5930) terinngathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^####100)


(5931) pentaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#5)


(5932) hexaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#6)


(5933) heptaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#7)


(5934) octaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#8)


(5935) ennaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#9)


(5936) dekaelgathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#10)

 

(5937) godtothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#100)

 

(5938) graltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^##100)

 

(5939) thraeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^###100)

 

(5940) terinntothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^####100)


(5941) pentaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#5)


(5942) hexaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#6)


(5943) heptaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#7)


(5944) octaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#8)


(5945) ennaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#9)


(5946) dekaeltothol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#10)


(5947) godtertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#100)

 

(5948) graltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^##100)


(5949) thraeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^###100)


(5950) terinntertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^####100)


(5951) pentaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#5)


(5952) hexaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#6)


(5953) heptaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#7)


(5954) octaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#8)


(5955) ennaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#9)


(5956) dekaeltertol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^#^#^#^#^#10)

 

(5957) godtopol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#6)

 

(5958) godhathor-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#7)

 

(5959) godheptol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#8)

 

(5960) godoctol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#9)


(5961) godentol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#10)


(5962) goddekathol-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#11)

 

(5963) tethrathoth-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#100)

 

(5964) grand-tethrathoth-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#100#2)


(5965) tethratrithoth-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#100#^^#100)


(5966) tethrathoth-by-hyperion-ex-terrible tethrathoth 

= E100#^^#>#(1+E100#^^#*#100)


(5967) deutero-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#*#^^#100)


(5968) trito-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#*#^^#*#^^#100)


(5969) teterto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#*#^^#*#^^#*#^^#100)


(5970) pepto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#5)


(5971) exto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#6)


(5972) epto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#7)


(5973) ogdo-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#8)


(5974) ento-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#9)


(5975) dekato-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#10)


(5976) tethrafact-ex-terrible tethrathoth 

= E100#^^#>#(1+E100(#^^#)^#100)


(5977) tethrathoth-ipso-godgahlah-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^#100)


(5978) tethrathoth-ipso-godgathor-ex-terrible tethrathoth 

= E100#^^#>#(1+E100(#^^#)^#^#^#100)


(5979) tethrathoth-ipso-godtothol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^#^#^#100)


(5980) tethrathoth-ipso-godtertol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#5)


(5981) tethrathoth-ipso-godtopol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#6)


(5982) tethrathoth-ipso-godhathor-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#7)


(5983) tethrathoth-ipso-godheptol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#8)


(5984) tethrathoth-ipso-godoctol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#9)


(5985) tethrathoth-ipso-godentol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#10)


(5986) tethrathoth-ipso-goddekathol-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#11)


(5987) tethrathoth-ipso-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^#^^#100)


(5988) tethrathoth-ipso-deutero-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#*#^^#)100)


(5989) tethrathoth-ipso-trito-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#*#^^#*#^^#)100)


(5990) tethrathoth-ipso-teterto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#*#^^#*#^^#*#^^#)100)


(5991) tethrathoth-ipso-pepto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#5)


(5992) tethrathoth-ipso-exto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#6)


(5993) tethrathoth-ipso-epto-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#7)


(5994) tethrathotho-ipso-ogdo-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#8)


(5995) tethrathoth-ipso-ento-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#9)


(5996) tethrathoth-ipso-dekato-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#10)

 

(5997) Monster-Giant-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^#100)


(5998) tethrathoth-ipso-tethrathoth-ipso-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^(#^^#)100)


(5999) Super Monster-Giant-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^(#^^#)^#100)


(6000) quadrupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^(#^^#)^(#^^#)^(#^^#)100)


(6001) quintupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#5)


(6002) sextupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#6)


(6003) septupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#7)


(6004) octupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#8)


(6005) nonupletetrated-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#9)


(6006) decupletetrated-tethrathoth-ex-terrible tethrathoth 

= E100#^^#>#(1+E100(#^^#)^^#10)

 

(6007) terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(#^^#)^^#100)

 

(6008) terrible-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100((#^^#)^^#)^^#100)

 

(6009) terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100(((#^^#)^^#)^^#)^^#100)

 

(6010) terrible-terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#5)


(6011) five-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#6)


(6012) six-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#7)


(6013) seven-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#8)


(6014) eight-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#9)


(6015) nine-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#10)


(6016) ten-ex-terrible-tethrathoth-ex-terrible tethrathoth

= E100#^^#>#(1+E100#^^#>#11)

                    The terrible operator is powerful ... and yet with our new name tethriterator, we can trivially beat all of this with a simple application of grand ...

 
(6017) grand tethriterator = E100#^^#>#100#2 
also called (6018) Great and Terrible tethrathoth

                    Expanding the expression we obtain...

E100#^^#>#100#2 = E100#^^#>#(E100#^^#>#100) 

= E100#^^#>#tethriterator

This means this number is also equivalent to ...

(6019) tethriterator-minus-one-ex-terrible tethrathoth

What's better than that...

(6020) tethriterator-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#>#100)

A tethriterator is just ninety-nine-ex-terrible tethrathoth so this is also equivalent to...

(6021) ninety-nine-ex-terrible-tethrathoth-ex-terrible tethrathoth

What's even better than that?

(6022) hundred-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#101)

So we can nest the -ex-terrible operator. Does that lead to anything new? ...

(6023) googol-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#(1+E100))

(6024) godgahlah-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#(1+E100#^#100))

... of coarse we can skip straight to ...

(6025) tethrathoth-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#(1+E100#^^#100))

(6026) terrible-tethrathoth-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#(1+E100(#^^#)^^#100))

This is still way less than...
 
(6027) grand grand tethriterator = E100#^^#>#100#3

= E100#^^#>#(E100#^^#>#100#2)

= E100#^^#>#(E100#^^#>#(E100#^^#>#100)

Furthermore...

(6028) tethrathoth-ex-terrible-tethrathoth-ex-terrible-tethrathoth-ex-terrible tethrathoth
= E100#^^#>#(1+E100#^^#>#(1+E100#^^#>#(1+E100#^^#100))

... is still way less than ...
 
(6029) triple-grand tethriterator = E100#^^#>#100#4

As you can see with our new delimiter, #^^#>#, we have no trouble keeping up with nestings of the the -ex-terrible operator! Nesting it only leads to one additional level of primitive recursion above LECEN. With xE^ however we can go much much MUCH FURTHER!!!

Using the grand operator repeatedly we can obtain a new sequence ...
 
(6030) quadruple-grand tethriterator = E100#^^#>#100#5
 
(6031) quintuple-grand tethriterator = E100#^^#>#100#6
 
(6032) sextuple-grand tethriterator = E100#^^#>#100#7
 
(6033) septuple-grand tethriterator = E100#^^#>#100#8
 
(6034) octuple-grand tethriterator = E100#^^#>#100#9

(6035) nonuple-grand tethriterator = E100#^^#>#100#10

(6036) decuple-grand tethriterator = E100#^^#>#100#11

...

(6037) vigintuple-grand tethriterator = E100#^^#>#100#21

(6038) trigintuple-grand tethriterator = E100#^^#>#100#31

(6039) quadragintuple-grand tethriterator = E100#^^#>#100#41

(6040) quinquagintuple-grand tethriterator = E100#^^#>#100#51

(6041) sexagintuple-grand tethriterator = E100#^^#>#100#61

(6042) septuagintuple-grand tethriterator = E100#^^#>#100#71

(6043) octogintuple-grand tethriterator = E100#^^#>#100#81

(6044) nonagintuple-grand tethriterator = E100#^^#>#100#91

...
 
Aarex extended this series up to the 7th member, sextuple-grand tethriterator, but this series is much more logically constructed and far easier to extend. It's also a trivial extension in any case as it is just the tethriterator sequence. We can easily jump to the hundred and first member of this sequence, and there is now a few ways to construct a name for it ...
 
(6045) centuple-grand tethriterator = E100#^^#>#100#101
also (6046) hundred-ex-grand tethriterator
 
In fact the -carta- operator can easily be used to extend much further and more generally. In fact we can quickly beat anything using tethrathoth, along with the terrible- and -ex- operators. Here are some examples of how our notation easily overcomes this now:
 
tethrathoth = E100#^^#>#1 = E100#^^#100
 
terrible tethrathoth = E100#^^#>#2 = E100(#^^#)^^#100
 
terrible terrible tethrathoth = E100#^^#>#3 = E100(#^^#)^^#)^^#100
 
(6047) three-ex-terrible tethrathoth = E100#^^#>#4
 
...
 
hundred-ex-terrible tethrathoth = E100#^^#>#101

 
googol-ex-terrible tethrathoth = E100#^^#>#(1+E100)

...
 
tethrathoth-ex-terrible tethrathoth = E100#^^#>#(1+E100#^^#100)
(~ E100#^^#>#100#2)
 
tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth
 
= E100#^^#>#(1+E100#^^#>#(1+E100#^^#100))
(~E100#^^#>#100#3)

                    ... the largest extension using this idea is found on my Ultimate Large Number List Part II. Namely ...

(6048)
tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth-ex-terrible tethrathoth

                    ... This amounts to exactly...

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

                ... this precise value does not admit of a compact form even in extended Cascading-E Notation (xE^), yet it does not extend LECEN as far as it might at first seem. All those +1s barely account for anything. One can delete all of them, and replace only the deepest nested one with +2, and still get a phenomenally larger value...

E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(E100#^^#>#(2+E100#^^#>#100)))))))))))))))))))))))))))))))))))))))))))))))))))))
 
                    ... this expression can be made more compact, using the rules of xE^...

E100#^^#>#(2+E100#^^#>#100)#53

                    ... this is still smaller than replacing 2+E100#^^#>#100 with E100#^^#>#100#2, which is much much larger...

E100#^^#>#(E100#^^#>#100#2)#53

                    ... this in turn can be simplified further...

E100#^^#>#(E100#^^#>#100#2)#53

E100#^^#>#(E100#^^#>#(E100#^^#>#100))#53

= E100#^^#>#100#55

                    ... as you can see, nesting the "-ex-terrible" operator barely registers in the grander scheme of xE^. This only accounts for a single additional level of primitive recursion. (6049) grangol-carta-tethriterator (E100#^^#>#100#100), is larger than even this, and grangol-carta-tethriterator pales in comparison to the -carta- operator can do...

but what if we go even further with nesting the "-ex-terrible" operator like what was done at the end of the Cascading-E Numbers article? What if we have...

(6050)
tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth

w/100 tethrathoth's

Well in the previous example there were 54 tethrathoth's yet it was beaten by E100#^^#>#100#55. So by the same argument this number would be less than E100#^^#>#100#101. So what if we had...

(6051)
tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth

w/tethrathoth tethrathoth's

That number would still be less than E100#^^#>#100#(1+tethrathoth). At this point a tethrathoth is rather paltry so we could also say this is much much less than E100#^^#>#100#tethriterator , which is E100#^^#>#100#(E100#^^#>#100), which could be simplified as E100#^^#>#100#1#2. Still not making much progress. Hmm... how about...

(6052)
tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth tethrathoth's

Well we know this will still be less than...

E100#^^#>#100#(1+E100#^^#>#100#(1+tethrathoth))

which is much less than...

E100#^^#>#100#(E100#^^#>#100#(2+tethrathoth))

which is much less than...

E100#^^#>#100#(E100#^^#>#100#tethriterator)

which can be rewritten as...

E100#^^#>#100#(E100#^^#>#100#1#2)

which can be rewritten as...

E100#^^#>#100#1#3

so yeah ... still going nowhere with these naive extensions. Okay fine. Time to bring out the BIG GUNS! Let's try...

(6053)
tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth-ex-terrible-tethrathoth-ex- ... -ex-terrible-tethrathoth-ex-terrible tethrathoth
tethrathoth's

w/tethrathoth tethrathoth's

where there are a tethrathoth lines

o_0;

Surely that must be freaking huge even in xE^, right?! Well did you notice how in the last two

 examples we only went from E100#^^#>#100#1#2 to E100#^^#>#100#1#3? So every 

time we add a line we are only incrementing the last argument by 1. Furthermore, when there

 were exactly 2 lines the argument was 2, and when there was exactly 3 lines the argument 

was 3. Therefore this number is STILL less than E100#^^#>#100#1#tethrathoth, which is 

smaller than E100#^^#>#100#1#tethriterator = E100#^^#>#1#1#2. As you can see 

iterating the -ex-terrible operator is no better than an ordinary recursion, which is no better

 than adding an extra hyperion. So not only can xE^ keep up with this, but even iterations of 

iterations of -ex-terrible, iterations of iterations of iterations of ex-terrible, and so on. 

                    The -carta- operator on the other hand will allow us to go much further. For example...

(6054) greagol-carta-tethriterator = E100#^^#>#100#100#100

... this would be like having a function which takes tethrathoth-ex-terrible tethrathoth-ex-terrible ... -ex-terrible tethrathoth, and then returned an expression with THAT many occurences of ex-terrible. Now repeat that a hundred times. This is only two levels of primitive recursion above LECEN. This is still smaller than our last entry but it still pales in comparison to our next entry...
 
(6055) gigangol-carta-tethriterator = E100#^^#>#100#100#100#100

Recall that the number we got with the tethrathoth lines was still way less than E100#^^#>#100#1#1#2. Yet gigangol-carta-tethriterator replaces those 1s and a 2 with 100s! And were just getting warmed up! Next we would have...

(6056) gorgegol-carta-tethriterator = E100#^^#>#100##5

(6057) gulgol-carta-tethriterator = E100#^^#>#100##6

(6058) gaspgol-carta-tethriterator = E100#^^#>#100##7

(6059) ginorgol-carta-tethriterator = E100#^^#>#100##8

(6060) gargantuul-carta-tethriterator = E100#^^#>#100##9

(6061) googondol-carta-tethriterator = E100#^^#>#100##10
 
...
 
(6062) gugolda-carta-tethriterator = E100#^^#>#100##100

(6063) gugolthra-carta-tethriterator = E100#^^#>#100###3

(6064) gugoltesla-carta-tethriterator = E100#^^#>#100###4

(6065) gugolpeta-carta-tethriterator = E100#^^#>#100###5

(6066) gugolhexa-carta-tethriterator = E100#^^#>#100###6

(6067) gugolhepta-carta-tethriterator = E100#^^#>#100###7

(6068) gugolocta-carta-tethriterator = E100#^^#>#100###8

(6069) gugolenna-carta-tethriterator = E100#^^#>#100###9

(6070) gugoldeka-carta-tethriterator = E100#^^#>#100###10

...

(6071) throogola-carta-tethriterator = E100#^^#>#100###100

(6072) tetroogola-carta-tethriterator = E100#^^#>#100####100

(6073) pentoogola-carta-tethriterator = E100#^^#>#100#^#5

(6074) hexoogola-carta-tethriterator = E100#^^#>#100#^#6

(6075) heptoogola-carta-tethriterator = E100#^^#>#100#^#7

(6076) ogdoogola-carta-tethriterator = E100#^^#>#100#^#8

(6077) entoogola-carta-tethriterator = E100#^^#>#100#^#9

(6078) dektoogola-carta-tethriterator = E100#^^#>#100#^#10
 
...
 
(6079) godgahlah-carta-tethriterator = E100#^^#>#100#^#100
 
(6080) grand-godgahlah-carta-tethriterator = E100#^^#>#100#^#100#2
 
= E100#^^#>#100#^#(godgahlah-carta-tehtriterator)
 
...
 
(6081) gridgahlah-carta-tethriterator = E100#^^#>#100#^##100
 
...
 
(6082) godgathor-carta-tethriterator = E100#^^#>#100#^#^#100
 
...
 
(6083) gralgathor-carta-tethriterator = E100#^^#>#100#^#^##100
 
...
 
(6084) tethrathoth-carta-tethriterator = E100#^^#>#100#^^#100
 
...
 
(6085) tethrathoth-dopplux-carta-tethriterator = E100#^^#>#100(#^^#)^(#^^#)100
 
(6086) Monster-Giant-carta-tethriterator = E100#^^#>#100(#^^#)^(#^^#)^#100
 
(6087) tethrathoth-trebletetrate-carta-tethriterator = E100#^^#>#100(#^^#)^^#3
 
(6088) tethrathoth-quadrupletetrate-carta-tethriterator = E100#^^#>#100(#^^#)^^#4
 
...
 
 
 (6089) terrible tethrathoth-carta-tethriterator = E100#^^#>#100(#^^#)^^#100

(6090) terrible terrible tethrathoth-carta-tethriterator 
= E100#^^#>#100((#^^#)^^#)^^#100

...

                    .... this brings us to (6091) tethriterator-carta-tethriterator or ...

(6092) tethritertri = E100#^^#>#100#^^#>#100

(6093) tethritertet = E100#^^#>#100#^^#>#100#^^#>#100 = E100#^^#>#*#4

(6094) tethriterpent = E100#^^#>#*#5

(6095) tethriterhex = E100#^^#>#*#6

(6096) tethriterhept = E100#^^#>#*#7

(6097) tethriteroct = E100#^^#>#*#8

(6098) tethriterenn = E100#^^#>#*#9

(6099) tethriterdeck = E100#^^#>#*#10 

...

(6100) tethriterhecate = E100#^^#>#*#100
(also (6101) tethritera-by-hyperion)

                ... this brings us to a whole new level...

(6102) tethritera-by-deutero-hyperion = E100#^^#>#*##100

(6103) tethritera-by-trito-hyperion = E100#^^#>#*###100

(6104) tethritera-by-teterto-hyperion = E100#^^#>#*####100

(6105) tethritera-by-pepto-hyperion = E100#^^#>#*#^#5

(6106) tethritera-by-exto-hyperion = E100#^^#>#*#^#6

(6107) tethritera-by-epto-hyperion = E100#^^#>#*#^#7

(6108) tethritera-by-ogdo-hyperion = E100#^^#>#*#^#8

(6109) tethritera-by-ento-hyperion = E100#^^#>#*#^#9

(6110) tethritera-by-dekato-hyperion = E100#^^#>#*#^#10

...

(6111) tethritera-by-hyperipso-hyperion = E100#^^#>#*#^#100
also (6112) tethriterator-by-godgahlah

(6113) tethritera-by-hyperipso-hyperion-by-hyperion = E100#^^#>#*#^#*#100
also (6114) tethriterator-by-godgahlah-by-hyperion

(6115) tethritera-by-hyperipso-hyperionby-deutero-hyperion = E100#^^#>#*#^#*##100
also (6116) tethriterator-by-godgahlah-by-deutero-hyperion

(6117) tethritera-by-hyperipso-hyperion-by-trito-hyperion = E100#^^#>#*#^#*###100
also (6118) tethriterator-by-godgahlah-by-trito-hyperion

(6119) tethritera-by-hyperipso-hyperion-by-teterto-hyperion 
= E100#^^#>#*#^#*####100
also (6120) tethriterator-by-godgahlah-by-teterto-hyperion

...

(6121) tethritera-by-hyperipso-hyperion-by-hyperada-hyperion 
= E100#^^#>#*#^#*#^#100
also (6122) tethriterator-by-godgahlah-by-godgahlah

...

(6123) tethritera-by-hyperipso-deutero-hyperion = E100#^^#>#*#^##100
also (6124) tethriterator-by-gridgahlah

(6125) tethritera-by-hyperipso-trito-hyperion = E100#^^#>#*#^###100
also (6126) tethriterator-by-kubikahlah

(6127) tethritera-by-hyperipso-teterto-hyperion = E100#^^#>#*#^####100
also (6128) tethriterator-by-quarticahlah

(6129) tethritera-by-hyperipso-pepto-hyperion = E100#^^#>#*#^#^#5
also (6130) tethriterator-by-quinticahlah

(6131) tethritera-by-hyperipso-exto-hyperion = E100#^^#>#*#^#^#6
also (6132) tethriterator-by-sexticahlah

(6133) tethritera-by-hyperipso-epto-hyperion = E100#^^#>#*#^#^#7
also (6134) tethriterator-by-septicahlah

(6135) tethritera-by-hyperipso-ogdo-hyperion = E100#^^#>#*#^#^#8
also (6136) tethriterator-by-octicahlah

(6137) tethritera-by-hyperipso-ento-hyperion = E100#^^#>#*#^#^#9
also (6138) tethriterator-by-nonicahlah

(6139) tethritera-by-hyperipso-dekato-hyperion = E100#^^#>#*#^#^#10
also (6140) tethriterator-by-decicahlah

...

(6141) tethritera-by-hyperipso-hyperipso-hyperion = E100#^^#>#*#^#^#100
also (6142) tethritera-by-hyperada-hecato-hyperion
also (6143) tethritera-by-hyper-tetradatri
also (6144) tethriterator-by-godgathor

(6145) tethritera-by-hyper-tetradatet = E100#^^#>#*#^#^#^#100
also (6146) tethriterator-by-godtothol

(6147) tethritera-by-hyper-tetradapent = E100#^^#>#*#^^#5
also (6148) tethriterator-by-godtertol

(6149) tethritera-by-hyper-tetradahex = E100#^^#>#*#^^#6
also (6150) tethriterator-by-godtopol

(6151) tethritera-by-hyper-tetradahept = E100#^^#>#*#^^#7
also (6152) tethriterator-by-godhathor

(6153) tethritera-by-hyper-tetrada-oct = E100#^^#>#*#^^#8
also (6154) tethriterator-by-godheptol

(6155) tethritera-by-hyper-tetrada-enn = E100#^^#>#*#^^#9
also (6156) tethriterator-by-godoctol

(6157) tethritera-by-hyper-tetrada-deck = E100#^^#>#*#^^#10
also (6158) tethriterator-by-godentol

(6159) tethriterator-by-goddekathol = E100#^^#>#*#^^#11

...

(6160) tethriterator-by-god-icosathol = E100#^^#>#*#^^#21

(6161) tethriterator-by-godtriantathol = E100#^^#>#*#^^#31

(6162) tethriterator-by-godsarantathol = E100#^^#>#*#^^#41

(6163) tethriterator-by-godpenintathol = E100#^^#>#*#^^#51

(6164) tethriterator-by-godexintathol = E100#^^#>#*#^^#61

(6165) tethriterator-by-godebdomintathol = E100#^^#>#*#^^#71

(6166) tethriterator-by-godogdontathol = E100#^^#>#*#^^#81

(6167) tethriterator-by-godenenintathol = E100#^^#>#*#^^#91

...

(6168) tethritera-by-tethrathoth = E100#^^#>#*#^^#100
also (6169) tethriterator-by-tethrathoth
also (6170) tethritera-by-hyper-tetrada-hecate

(6171) tethritera-by-terrible-tethrathoth  = E100#^^#>#*(#^^#)^^#100

(6172) tethritera-by-terrible-terrible-tethrathoth = E100#^^#>#*((#^^#)^^#)^^#100

(6173) tethritera-by-triterrible-tethrathoth = E100#^^#>#*(((#^^#)^^#)^^#)^^#100

(6174) tethritera-by-tetraterrible-tethrathoth = E100#^^#>#*#^^#>#5

(6175) tethritera-by-pentaterrible-tethrathoth = E100#^^#>#*#^^#>#6

(6176) tethritera-by-hexaterrible-tethrathoth = E100#^^#>#*#^^#>#7

(6177) tethritera-by-heptaterrible-tethrathoth = E100#^^#>#*#^^#>#8

(6178) tethritera-by-octaterrible-tethrathoth = E100#^^#>#*#^^#>#9

(6179) tethritera-by-ennaterrible-tethrathoth = E100#^^#>#*#^^#>#10

(6180) tethritera-by-dekaterrible-tethrathoth = E100#^^#>#*#^^#>#11

...

(6181) deutero-tethriterator = E100#^^#>#*#^^#>#100
also (6182) tethritera-tethriterator
also (6183) tethritera-by-hectaterrible-tethrathoth

            ... this brings us to yet another higher level of diagonalization, still within thetethriterator group...

(6184) trito-tethriterator = E100#^^#>#*#^^#>#*#^^#>#100

(6185) teterto-tethriterator = E100#^^#>#*#^^#>#*#^^#>#*#^^#>#100

(6186) pepto-tethriterator = E100(#^^#>#)^#5

(6187) exto-tethriterator = E100(#^^#>#)^#6

(6188) epto-tethriterator = E100(#^^#>#)^#7

(6189) ogdo-tethriterator = E100(#^^#>#)^#8

(6190) ento-tethriterator = E100(#^^#>#)^#9

(6191) dekato-tethriterator = E100(#^^#>#)^#10

...

(6192) isosto-tethriterator = E100(#^^#>#)^#20

(6193) trianto-tethriterator = E100(#^^#>#)^#30

(6194) saranto-tethriterator = E100(#^^#>#)^#40

(6195) peninto-tethriterator = E100(#^^#>#)^#50

(6196) exinto-tethriterator = E100(#^^#>#)^#60

(6197) ebdominto-tethriterator = E100(#^^#>#)^#70

(6198) ogdonto-tethriterator = E100(#^^#>#)^#80

(6199) eneninto-tethriterator = E100(#^^#>#)^#90

...

(6200) hecato-tethriterator = E100(#^^#>#)^#100

                    ... next an even faster sequence ...

(6201) tethriterfact = E100(#^^#>#)^#100

(6202) grideutertethriterator = E100(#^^#>#)^##100

(6203) kubicutethriterator = E100(#^^#>#)^###100

(6204) quarticutethriterator = E100(#^^#>#)^####100

(6205) quinticutethriterator = E100(#^^#>#)^#^#5

(6206) sexticutethriterator = E100(#^^#>#)^#^#6

(6207) septicutethriterator = E100(#^^#>#)^#^#7

(6208) octicutethriterator = E100(#^^#>#)^#^#8

(6209) nonicutethriterator = E100(#^^#>#)^#^#9

(6210) decicutethriterator = E100(#^^#>#)^#^#10

...

(6211) viginticutethriterator= E100(#^^#>#)^#^#20

(6212) triginticutethriterator = E100(#^^#>#)^#^#30

(6213) quadraginticutethriterator = E100(#^^#>#)^#^#40

(6214) quinquaginticutethriterator = E100(#^^#>#)^#^#50

(6215) sexaginticutethriterator = E100(#^^#>#)^#^#60

(6216) septuaginticutethriterator = E100(#^^#>#)^#^#70

(6217) octoginticutethriterator = E100(#^^#>#)^#^#80

(6218) nonaginticutethriterator = E100(#^^#>#)^#^#90

(6219) centicutethriterator = E100(#^^#>#)^#^#100

                        ... next on to even more gargantuan numbers ...

(6220) tethritergodgathor = E100(#^^#>#)^#^#100

(6221) tethritergralgathor = E100(#^^#>#)^#^##100

(6222) tethritergodtothol = E100(#^^#>#)^#^#^#100

(6223) tethritertethrathoth = E100(#^^#>#)^#^^#100

(6224) tethriter-Monster-Giant = E100(#^^#>#)^(#^^#)^#100

(6225) tethriter-terri-tethrathoth = E100(#^^#>#)^(#^^#)^^#100

(6226) tethriter-duterri-tethrathoth = E100(#^^#>#)^((#^^#)^^#)^^#100

(6227) tethriter-triterri-tethrathoth = E100(#^^#>#)^(#^^#>#)4

(6228) tethriterator-dubletetrate = E100(#^^#>#)^(#^^#>#)100

(6229) tethriterator-trebletetrate = E100(#^^#>#)^^#3

(6230) tethriterator-quadrupletetrate = E100(#^^#>#)^^#4

(6231) tethriterator-quintupletetrate = E100(#^^#>#)^^#5

(6232) tethriterator-sextupletetrate = E100(#^^#>#)^^#6

(6233) tethriterator-septupletetrate = E100(#^^#>#)^^#7

(6234) tethriterator-octupletetrate = E100(#^^#>#)^^#8

(6235) tethriterator-nonupletetrate = E100(#^^#>#)^^#9

(6236) tethriterator-decupletetrate = E100(#^^#>#)^^#10

...

(6237) terrible tethriterator = E100(#^^#>#)^^#100

(6238) terrible terrible tethriterator = E100((#^^#>#)^^#)^^#100

(6239) terrible terrible terrible tethriterator = E100(((#^^>#)^^#)^^#)^^#100

(6240) terrible terrible terrible terrible tethriterator = E100((((#^^#>#)^^#)^^#)^^#)^^#100

(6241) five-ex-terrible tethriterator

= E100#^^#>(#+#)5

(6242) six-ex-terrible tethriterator

= E100#^^#>(#+#)6

(6243) seven-ex-terrible tethriterator

= E100#^^#>(#+#)7

(6244) eight-ex-terrible tethriterator

= E100#^^#>(#+#)8

(6245) nine-ex-terrible tethriterator

= E100#^^#>(#+#)9

(6246) ten-ex-terrible tethriterator

= E100#^^#>(#+#)10

...

Now imagine the number ...

E100(((...(((#^^#>#)^^#)^^#)^^# ... ^^#)^^#)^^#100 w/100 ^^#s

using xE^ we can now truncate this to...

E100#^^#>(#+#)100

                    This brings us to the next level of recursion. We can begin to stack larger and larger hyperion expressions on top of #^^#. Here we go ...

(6247) tethriditerator = E100#^^#>(#+#)100

(6248) terrible tethriditerator = E100(#^^#>(#+#))^^#100

(6249) terrible terrible tethriditerator = E100((#^^#>(#+#))^^#)^^#100

(6250) terrible terrible terrible tethriditerator = E100(((#^^#>(#+#))^^#)^^#)^^#100

(6251) terrible terrible terrible terrible tethriditerator 

= E100((((#^^#>(#+#))^^#)^^#)^^#)^^#100

(6252) five-ex-terrible tethriditerator

= E100#^^#>(#+#+#)5

(6253) six-ex-terrible tethriditerator

= E100#^^#>(#+#+#)6

(6254) seven-ex-terrible tethriditerator

= E100#^^#>(#+#+#)7

(6255) eight-ex-terrible tethriditerator

= E100#^^#>(#+#+#)8

(6256) nine-ex-terrible tethriditerator

= E100#^^#>(#+#+#)9

(6257) ten-ex-terrible tethriditerator

= E100#^^#>(#+#+#)10

...

(6258) tethritriterator = E100#^^#>(#+#+#)100

(6259) terrible tethritriterator = E100(#^^#>(#+#+#))^^#100

(6260) terrible terrible tethritriterator = E100((#^^#>(#+#+#))^^#)^^#100

(6261) terrible terrible terrible tethritriterator = E100(((#^^#>(#+#+#))^^#)^^#)^^#100

(6262) terrible terrible terrible terrible tethritriterator 

= E100((((#^^#>(#+#+#))^^#)^^#)^^#)^^#100

(6263) five-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)5

(6264) six-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)6

(6265) seven-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)7

(6266) eight-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)8

(6267) nine-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)9

(6268) ten-ex-terrible tethritriterator

= E100#^^#>(#+#+#+#)10

...

(6269) tethriquaditerator = E100#^^#>(#+#+#+#)100

(6270) tethriquiditerator = E100#^^#>##5

(6271) tethrisiditerator = E100#^^#>##6

(6272) tethrisepiterator = E100#^^#>##7

(6273) tethriogditerator = E100#^^#>##8

(6274) tethrinoniterator = E100#^^#>##9

(6275) tethrideciterator = E100#^^#>##10

...

 ... even higher diagonalizations ...

(6276) tethrigriditerator = E100#^^#>##100

(6277) tethricubiculator = E100#^^#>###100

(6278) tethriquarticulator = E100#^^#>####100

(6279) tethriquinticulator = E100#^^#>#^#5

(6280) tethrisexticulator = E100#^^#>#^#6

(6281) tethrisepticulator = E100#^^#>#^#7

(6282) tethriocticulator = E100#^^#>#^#8

(6283) tethrinoniculator = E100#^^#>#^#9

(6284) tethrideciculator = E100#^^#>#^#10

...

(6285) tethricenticulator = E100#^^#>#^#100

... meanwhile in the next next dimension ...

(6286) tethrispatialator = E100#^^#>#^#100

(6287) tethrispatial-squarediterator = E100#^^#>(#^#*#^#)100

(6288) tethrispatial-cubiculator = E100#^^#>(#^#*#^#*#^#)100

(6289) tethrispatial-quarticulator = E100#^^#>(#^#*#^#*#^#*#^#)100

(6290) tethrispatial-quinticulator = E100#^^#>#^##5

(6291) tethrispatial-sexticulator = E100#^^#>#^##6

(6292) tethrispatial-septiculator = E100#^^#>#^##7

(6293) tethrispatial-octiculator = E100#^^#>#^##8

(6294) tethrispatial-noniculator = E100#^^#>#^##9

(6295) tethrispatial-deciculator = E100#^^#>#^##10

(6296) tethrispatial-centiculator = E100#^^#>#^##100

... we still have quite a climb left to reach #^^## ...

(6297) tethrideuterspatialator = E100#^^#>#^##100

(6298) tethritritospatialator = E100#^^#>#^###100

(6299) tethritetertospatialator = E100#^^#>#^####100

(6300) tethripeptospatialator = E100#^^#>#^#^#5

(6301) tethri-extospatialator = E100#^^#>#^#^#6

(6302) tethri-eptospatialator = E100#^^#>#^#^#7

(6303) tethri-ogdospatialator = E100#^^#>#^#^#8

(6304) tethri-entospatialator = E100#^^#>#^#^#9

(6305) tethri-dekatospatialator = E100#^^#>#^#^#10

...

(6306) tethri-isostospatialator = E100#^^#>#^#^#20

(6307) tethri-triantospatialator = E100#^^#>#^#^#30

(6308) tethri-sarantospatialator = E100#^^#>#^#^#40

(6309) tethri-penintospatialator = E100#^^#>#^#^#50

(6310) tethri-exintospatialator = E100#^^#>#^#^#60

(6311) tethri-ebdomintospatialator = E100#^^#>#^#^#70

(6312) tethri-ogdontospatialator = E100#^^#>#^#^#80

(6313) tethri-enenintospatialator = E100#^^#>#^#^#90

...

(6314) tethri-hecatospatialator = E100#^^#>#^#^#100

... and another even higher level of diagonalization ...

(6315) tethri-superspatialator = E100#^^#>#^#^#100

(6316) tethri-quadratetratediterator = E100#^^#>#^#^#^#100

(6317) tethri-quintatetratediterator = E100#^^#>#^^#5

(6318) tethri-sextatetratediterator = E100#^^#>#^^#6

(6319) tethri-septatetratediterator = E100#^^#>#^^#7

(6320) tethri-octatetratediterator = E100#^^#>#^^#8

(6321) tethri-nonatetratediterator = E100#^^#>#^^#9

(6322) tethri-decatetratediterator = E100#^^#>#^^#10

...

(6323) tethri-vigintatetratediterator = E100#^^#>#^^#20

...

(6324) tethri-centatetratediterator = E100#^^#>#^^#100

                    In a very loose sense we can think of this as a double stack tetrational tower. ' #^^#>#^^# ' can be interpreted as #^^(#+#), and thus as the hypothetical ordinal w^^(w*2). However do not mistake this for a mere #^^200. That value can easily be defined as E100#^^#200 = E100#^^#[200]100 = E100#^^(200)100. That value however is already vastly smaller than a grand tethrathoth, which is E100#^^(tethrathoth)100. Remember that ordinal hyper-operations are far more complex than the hyper-operations applied to the integers! Tethri-centatetratediterator would first have to expand the #^^# on top of the stack. This must then decompose into iterations of the ^^# operator on yet smaller hyperialshyperial is an ordinal written using hyperions and hyperion operators. Let's look at some of the expansion...

E100#^^#>#^^#100 =

E100#^^#>#^^(100)100 =

E100#^^#>#^#^ ... ^#^#^#100 =

E100#^^#>#^#^ ... ^#^#100100 =

E100#^^#>#^#^ ... ^(#^#99*#^#99* ... #^#99*#^#99)100 =

E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)100)100 =

E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99*(#^#97)100)100 =

...

E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99* ... *(#^#2)99*(#^#)99*#^#)100 =

E100#^^#>#^#^ ... ^((#^#99)99*(#^#98)99* ... *(#^#2)99*(#^#)99*#100)100

                    ... at this point the decomposition cascades down to the next level although much more complex than before. You'll notice that the decomposition follows very similar behavior to the goodstein sequence. The decomposition here is also identical to that of #^^# in a tethrathoth. However once this collapse reaches the form &*#, we do not simply expand using the expansion rule as in tethrathoth. Instead we aren't even done collapsing the hyperial above the stack. It proceeds as follows:

E100#^^#>(&*#)100 =

E100#^^#>(&+&+&+ ... +&+&+&)100 w/100 &s

                ... now & must itself decompose into a series of additions. This continues for a very long time until we eventually reachthe form &+#. At this point we get...

E100#^^#>(&+#)100 =

E100(#^^#>&)^^#>#100 =

E100(#^^#>&)^^#>(100)100 =

E100(((...(((#^^#>&)^^#)^^#)^^#) ... )^^#)^^#)^^#100 w/100 ^^#s after #^^#>&

the decomposition of & temporarily halts here as the ^^# need to be resolved first. This leads to a massive power tower, which keeps growing and growing as ^^# operators are resolved. This goes on while & further expands into even more ^^# operators. Finally at the pinnacle of this unfathomably larger tower would be #^^# ... but then the real nightmare has only begun as the entire super-cascade itself made up of cascading components must very slowly decay. The process becomes hazy out there but what we do know is thateventually it must reduce to (#^^#)^& for some extremely complicated and long winded &. Please note that & is NOT a number but a hyperiate. It will also NOT be something "simple" like (#^^#)^(#^^#)^(#^^#)^...^(#^^#)^(#^^#) with a huge number of #^^#s. The delimiter we'll rather involve a lot of mixed expressions. Generally speaking things will get frighteningly complicated before they become simple and repetitive. This only happens whenever we get to apply the recursive rule. This is the rule that actually increases the size of the last argument. Of coarse the last argument will continue to return to the value of 100 because the first argument is 100. The huge value then get's stored in the delimiter by the number of repetitions until it feeds back into the last argument. The processes are far too long for us to ever have a complete picture of it. However we can at least know that it will return to certain forms which we can describe. eventually we would reach...

E100#^^#X

where X is a tremendous value, virtually indistinguishable for mere mortals such as us from tehtri-centatetratediterator itself! Suffice it to say that X is MUCH MUCH bigger than 200!

                We STILL have not reached #^^##! Let's continue. We now introduce an even higher level of diagonalization, by introducing the staculate and turret operators ...

(6325) dustaculated-tethrathoth = E100#^^#>#^^#100

(6326) terrible-tethrathothiturreted-tethrathoth = E100#^^#>(#^^#)^^#100

(6327) double-terrible-tethrathothiturreted-tethrathoth = E100#^^#>((#^^#)^^#)^^#100

                        The staculate-operator forms a stack of the specified hyper-ordinal. This is in the form ' #-staculated-@ ' and is mapped to the number E100@>@> ... >@>@100 with # repetitions of @. The turret-operator allows for even greater specification. ' @-turreted-% ' means %>@. This works even if % and/or @ also includes carrot tops. A turret is a small tower that rests above a fortifying wall. Thus @ is turreted to %. Some further examples ... 

...

(6328) tethriter-turreted-tethrathoth = E100#^^#>#^^#>#100

note that the second caret top must be resolved before the first. The correct order of operations is therefore ...

#^^#>(#^^#>#)

 Moving on we have...

(6329) terrible tethriter-turreted-tethrathoth = E100(#^^#>#^^#>#)^^#100

... this should not be confused with ...

E100#^^#>(#^^#>#)^^#100

(we'll see this number on the list shortly)

... this does not mean the same thing and is in fact much larger. Again all operators resolve from right to left and therefore the correct order of operations is ...

#^^#>((#^^#>#)^^#)

... moving on ...

(6330) double-terrible tethriter-turreted-tethrathoth = E100((#^^#>#^^#>#)^^#)^^#100

...

(6331) hundred-ex-terrible tethriter-turreted-tethrathoth = E100#^^#>(#^^#>#+#)100

...

(6332) godgahlah-teriterated-tethriterator-turreted-tethrathoth

= E100#^^#>(#^^#>#+#^#)100

(6333) tethrathoth-teriterated-tethriterator-turreted-tethrathoth

= E100#^^#>(#^^#>#+#^^#)100

(6334) Monser-Giant-teriterated-tethriterator-turreted-tethrathoth

= E100#^^#>(#^^#>#+(#^^#)^(#^^#)^#)100

(6335) tethriterator-teriterated-tethriterator-turreted-tethrathoth 

= E100#^^#>(#^^#>#+#^^#>#)100

...

(6336) tethriterator-by-hyperion-turreted-tethrathoth

= E100#^^#>(#^^#>#*#)100

(6337) tethriterator-by-godgahlah-turreted-tethrathoth

= E100#^^#>(#^^#>#*#^#)100

(6338) tethriterator-by-tethrathoth-turreted-tethrathoth

= E100#^^#>(#^^#>#*#^^#)100

(6339) tethriterator-by-Monster-Giant-turreted-tethrathoth

= E100#^^#>(#^^#>#*(#^^#)^(#^^#)^#)100

(6340) tethriterator-by-terrible-tethrathoth-turreted-tethrathoth

= E100#^^#>(#^^#>#*(#^^#)^^#)100

...

(6341) deutertethriter-turreted-tethrathoth = E100#^^#>(#^^#>#*#^^#>#)100

... not to be confused with ...

(6342) deutero tethriter-turreted-tethrathoth = E100#^^#>#^^#>#*#^^#>#^^#>#100

... which is much smaller ...

(6343) tritetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#3

(6344) tetertetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#4

(6345) peptetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#5

(6346) extetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#6

(6347) eptetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#7

(6348) ogdetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#8

(6349) entetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#9

(6350) dekatetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#10

...

(6351) hecatetethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^#100

...

(6352) territethriter-turreted-tethrathoth = E100#^^#>(#^^#>#)^^#100

(6353) duterritethriter-turreted-tethrathoth = E100#^^#>((#^^#>#)^^#)^^#100

...

(6354) tethriditer-turreted-tethrathoth = E100#^^#>#^^#>(#+#)100

(6355) tethritriter-turreted-tethrathoth = E100#^^#>#^^#>(#+#+#)100

(6356) tethriquaditer-turreted-tethrathoth = E100#^^#>#^^#>(#+#+#+#)100

(6357) tethriquiditer-turreted-tethrathoth = E100#^^#>#^^#>##5

(6358) tethrisiditer-turreted-tethrathoth = E100#^^#>#^^#>##6

(6359) tethrisepiter-turreted-tethrathoth = E100#^^#>#^^#>##7

(6360) tethri-ogditer-turreted-tethrathoth = E100#^^#>#^^#>##8

(6361) tethri-noniter-turreted-tethrathoth = E100#^^#>#^^#>##9

(6362) tethri-deciter-turreted-tethrathoth = E100#^^#>#^^#>##10 

...

(6363) tethrigriditer-turreted-tethrathoth = E100#^^#>#^^#>##100

(6364) tethricubicu-turreted-tethrathoth = E100#^^#>#^^#>###100

(6365) tethriquarticu-turreted-tethrathoth = E100#^^#>#^^#>####100 

(6366) tethriquinticu-turreted-tethrathoth = E100#^^#>#^^#>#^#5

(6367) tethrisexticu-turreted-tethrathoth = E100#^^#>#^^#>#^#6

(6368) tethrisepticu-turreted-tethrathoth = E100#^^#>#^^#>#^#7

(6369) tethri-octicu-turreted-tethrathoth = E100#^^#>#^^#>#^#8

(6370) tethrinonicu-turreted-tethrathoth = E100#^^#>#^^#>#^#9

(6371) tethridecicu-turreted-tethrathoth = E100#^^#>#^^#>#^#10

...

(6372) tethrispatialaturreted-tethrathoth = E100#^^#>#^^#>#^#100

(6373) tethrideuterspatialaturreted-tethrathoth = E100#^^#>#^^#>#^##100

(6374) tethritritospatialaturreted-tethrathoth = E100#^^#>#^^#>#^###100

(6375) tethritetertospatialaturreted-tethrathoth = E100#^^#>#^^#>#^####100

...

(6376) tethri-superspatialaturreted-tethrathoth = E100#^^#>#^^#>#^#^#100

(6377) tethriquadratetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^#^#^#100

(6378) tethriquintatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#5

(6379) tethrisextatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#6

(6380) tethriseptatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#7

(6381) tethrioctatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#8

(6382) tethrinonatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#9

(6383) tethridecatetratediter-turreted-tethrathoth = E100#^^#>#^^#>#^^#10

                Here we reach the end of this approach. We now can use the staculate-operator to finish up the tethriterator group ...

(6384) tristaculated-tethrathoth = E100#^^#>#^^#>#^^#100

(6385) territethrathothiturreted-dustaculated-tethrathoth 

= E100#^^#>#^^#>(#^^#)^^#100

(6386) tethriterturreted-dustaculated-tethrathoth = E100#^^#>#^^#>#^^#>#100

...

(6387) tetrastaculated-tethrathoth = E100#^^#>#^^#>#^^#>#^^#100

(6388) tethriterturreted-tristaculated-tethrathoth = E100#^^#>#^^#>#^^#>#^^#>#100

(6389) pentastaculated-tethrathoth = E100#^^##5

(6390) hexastaculated-tethrathoth = E100#^^##6

(6391) heptastaculated-tethrathoth = E100#^^##7

(6392) ogdastaculated-tethrathoth = E100#^^##8

(6393) ennastaculated-tethrathoth = E100#^^##9

(6394) dekastaculated-tethrathoth = E100#^^##10

...

(6395) icosastaculated-tethrathoth = E100#^^##20

(6396) triantastaculated-tethrathoth = E100#^^##30

(6397) sarantastaculated-tethrathoth = E100#^^##40

(6398) penintastaculated-tethrathoth = E100#^^##50

(6399) exintastaculated-tethrathoth = E100#^^##60

(6400) ebdomintastaculated-tethrathoth = E100#^^##70

(6401) ogdontastaculated-tethrathoth = E100#^^##80

(6402) enenintastaculated-tethrathoth = E100#^^##90

...

(6403) hecatastaculated-tethrathoth = E100#^^##100

...

(6404) Berlin Wall = E100#^^##100,000,000 =

E100#^^#>#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#>#^^#100

w/100,000,000 #^^#s

... this expression would be roughly 7 to 8 times the length of the real berlin wall which stretched for about 100 miles ...

(6405) grand Berlin Wall = E100#^^##100,000,000#2 =

E100#^^##(E100#^^##100,000,000) = E100#^^##(Berlin Wall) =

E100#^^#>#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#>#^^#100

w/Berlin Wall #^^#s

... this expression ... stretches further than the diameter of the observable universe-- no scratch that, scale up from the Berlin Wall to the observable universe as many times as there are particles in the observable universe -- no scratch that, find out how many particles THAT would contain, scale up that many times then find out how many particles -- ah, fuck it, we left analogies like this behind AGES ago. There is no possible way for mere mortals such as us to unpack this completely ... moving on ...


We have already completely exhausted and transcended LECEN ... but we are just getting started with xE^ ...


Tethracross Regiment

Category 61

Members: 291

(6406 - 6696)



φ(2,0)



 ... at last we reach #^^##, identified at the closing of the Cascading-E article as the foundation of formulating xE^. Before we could not provide a fundamental sequence for it. Now we can say ...

#^^##[n] = #^^#>#^^#>#^^#> ... >#^^#>#^^# w/n #^^#s

Aarex instead of giving it a fundamental sequence treated it as a mere synonym. This makes it significantly less powerful.

In any case we can now define the following googolism ...

(6406) tethracross = E100#^^##100

also sometimes called (6407) tethrasquare

this is also equivalent to hecatastaculated-tethrathoth

this expands to...

E100#^^#>#^^#>#^^#> ... ... >#^^#>#^^#>#^^#100 w/100 #^^#s

This number is on the order of φ(2,0)

... we can continue by using all the standard constructions up to this point ...

(6408) grand tethracross = E100#^^##100#2

(6409) grangol-carta-tethracross = E100#^^##100#100

(6410) godgahlah-carta-tethracross = E100#^^##100#^#100

(6411) tethrathoth-carta-tethracross = E100#^^##100#^^#100

(6412) tethriterator-carta-tethracross = E100#^^##100#^^#>#100

 

...

 

(6413) tethracross-by-deuteron = E100#^^##100#^^##100

(6414) tethracross-by-triton = E100#^^##100#^^##100#^^##100

(6415) tethracross-by-teterton = E100#^^##*#5

(6416) tethracross-by-pepton = E100#^^##*#6

(6417) tethracross-by-exton = E100#^^##*#7

(6418) tethracross-by-epton = E100#^^##*#8

(6419) tethracross-by-ogdon = E100#^^##*#9

(6420) tethracross-by-enton = E100#^^##*#10

(6421) tethracross-by-dekaton = E100#^^##*#11

...

(6422) deutero-tethracross = E100#^^##*#^^##100

(6423) trito-tethracross = E100#^^##*#^^##*#^^##100

(6424) teterto-tethracross = E100#^^##*#^^##*#^^##*#^^##100

(6425) pepto-tethracross = E100(#^^##)^#5

(6426) exto-tethracross = E100(#^^##)^#6

(6427) epto-tethracross = E100(#^^##)^#7

(6428) ogdo-tethracross = E100(#^^##)^#8

(6429) ento-tethracross = E100(#^^##)^#9

(6430) dekato-tethracross = E100(#^^##)^#10

...

(6431) isosto-tethracross = E100(#^^##)^#20

(6432) trianto-tethracross = E100(#^^##)^#30

(6433) saranto-tethracross = E100(#^^##)^#40

(6434) peninto-tethracross = E100(#^^##)^#50

(6435) exinto-tethracross = E100(#^^##)^#60

(6436) ebdominto-tethracross = E100(#^^##)^#70

(6437) ogdonto-tethracross = E100(#^^##)^#80

(6438) eneninto-tethracross = E100(#^^##)^#90

...

(6439) hecato-tethracross = E100(#^^##)^#100

...

(6440) tethracruxifact = E100(#^^##)^#100

(6441) grideutertethracross = E100(#^^##)^##100

alternatively (6442) tethracruxigrid

(6443) kubicutethracross = E100(#^^##)^###100

alternatively (6444) tethracruxicube

(6445) quarticutethracross = E100(#^^##)^####100

alternatively (6446) tethracruxitess

(6447) quinticutethracross = E100(#^^##)^#^#5

(6448) sexticutethracross = E100(#^^##)^#^#6

(6449) septicutethracross = E100(#^^##)^#^#7

(6450) octicutethracross = E100(#^^##)^#^#8

(6451) nonicutethracross = E100(#^^##)^#^#9

(6452) decicutethracross = E100(#^^##)^#^#10

...

(6453) centicutethracross = E100(#^^##)^#^#100

...

(6454) tethracross-ad-gridgahlahium = E100(#^^##)^#^##100

(6455) tethracross-ad-kubikahlahium = E100(#^^##)^#^###100

(6456) tethracross-ad-quarticahlahium = E100(#^^##)^#^####100

...

(6457) tethracross-ad-godgathorium = E100(#^^##)^#^#^#100

(6458) tethracross-ad-godtotholium = E100(#^^##)^#^#^#^#100

(6459) tethracross-ad-godtertolium = E100(#^^##)^#^#^#^#^#100

(6460) tethracross-ad-godtopolium = E100(#^^##)^#^^#6

(6461) tethracross-ad-godhathorium = E100(#^^##)^#^^#7

(6462) tethracross-ad-godheptolium = E100(#^^##)^#^^#8

(6463) tethracross-ad-godoctolium = E100(#^^##)^#^^#9

(6464) tethracross-ad-godentolium = E100(#^^##)^#^^#10

(6465) tethracross-ad-goddekatholium = E100(#^^##)^#^^#11

...

(6466) tethracross-ad-tethrathothium = E100(#^^##)^#^^#100

(6467) tethracross-ad-Monster-Giantium = E100(#^^##)^(#^^#)^(#^^#)^#100

(6468) tethracross-ad-terrible-tethrathothium = E100(#^^##)^(#^^#)^^#100

(6469) tethracross-ad-terrible-terrible-tethrathothium 

= E100(#^^##)^((#^^#)^^#)^^#100

...

(6470) tethracross-ad-tethriteratorium = E100(#^^##)^#^^#>#100

(6471) tethracross-ad-tethriditeratorium = E100(#^^##)^#^^#>(#+#)100

(6472) tethracross-ad-tethraspatialatorium = E100(#^^##)^#^^#>#^#100

...

(6473) tethracross-ad-dustaculated-tethrathothium = E100(#^^##)^#^^#>#^^#100

(6474) tethracross-ad-tristaculated-tethrathothium 

= E100(#^^##)^#^^#>#^^#>#^^#100

(6475) tethracross-ad-tetrastaculated-tethrathothium

= E100(#^^##)^#^^#>#^^#>#^^#>#^^#100

(6476) tethracross-ad-pentastaculated-tethrathothium = E100(#^^##)^#^^##5

(6477) tethracross-ad-hexastaculated-tethrathothium = E100(#^^##)^#^^##6

(6478) tethracross-ad-heptastaculated-tethrathothium = E100(#^^##)^#^^##7

(6479) tethracross-ad-octastaculated-tethrathothium = E100(#^^##)^#^^##8

(6480) tethracross-ad-ennastaculated-tethrathothium = E100(#^^##)^#^^##9

(6481) tethracross-ad-dekastaculated-tethrathothium = E100(#^^##)^#^^##10

...

(6482) dutetrated-tethracross = E100(#^^##)^(#^^##)100

(6483) tritetrated-tethracross = E100(#^^##)^(#^^##)^(#^^##)100

(6484) quadratetrated-tethracross = E100(#^^##)^(#^^##)^(#^^##)^(#^^##)100

(6485) quinquatetrated-tethracross = E100(#^^##)^^#5

(6486) sexatetrated-tethracross = E100(#^^##)^^#6

(6487) septatetrated-tethracross = E100(#^^##)^^#7

(6488) octatetrated-tethracross = E100(#^^##)^^#8

(6489) nonatetrated-tethracross = E100(#^^##)^^#9

(6490) decatetrated-tethracross = E100(#^^##)^^#10

...

(6491) terrible tethracross = E100(#^^##)^^#100

(6492) terrible terrible tethracross = E100((#^^##)^^#)^^#100

...

(6493) hundred-ex-terrible tethracross = E100(#^^##)^^#>#100

...

(6494) hundred-ex-terrible territethracross = E100(#^^##)^^#)^^#>#100

*Note that E100((#^^##)^^#)^^#>#100 is equivalent to E100(#^^##)^^#>#101

... 

(6495) tethrathoth-ex-terrible tethracross = E100(#^^##)^^#>#(E100#^^#100)

(6496) tethracross-ex-terrible tethracross = E100(#^^##)^^#>#(E100#^^##100)

... to go further we allow previous googolism's to act as operators on newer googolism's in a way that is analogous to how xE^ takes ordinals and applies previous operators to generate new ordinals ...

(6497) tethriterated-tethracross = E100(#^^##)^^#>#100

(6498) grand tethriterated-tethracross = E100(#^^##)^^#>#100#2

...

(6499) tethriditerated-tethracross = E100(#^^##)^^#>(#+#)100

(6500) tethritriterated-tethracross = E100(#^^##)^^#>(#+#+#)100

(6501) tethriquaditerated-tethracross = E100(#^^##)^^#>(#+#+#+#)100

(6502) tethriquiditerated-tethracross = E100(#^^##)^^#>##5

(6503) tethrisiditerated-tethracross = E100(#^^##)^^#>##6

(6504) tethrisepiterated-tethracross = E100(#^^##)^^#>##7

(6505) tethri-ogditerated-tethracross = E100(#^^##)^^#>##8

(6506) tethri-noniterated-tethracross = E100(#^^##)^^#>##9

(6507) tethri-deciterated-tethracross = E100(#^^##)^^#>##10

...

(6508) tethrigriditerated-tethracross = E100(#^^##)^^#>##100

(6509) tethricubiculated-tethracross = E100(#^^##)^^#>###100

(6510) tethriquarticulated-tethracross = E100(#^^##)^^#>####100

(6511) tethriquinticulated-tethracross = E100(#^^##)^^#>#^#5

(6512) tethrisexticulated-tethracross = E100(#^^##)^^#>#^#6

(6513) tethrisepticulated-tethracross = E100(#^^##)^^#>#^#7

(6514) tethri-octiculated-tethracross = E100(#^^##)^^#>#^#8

(6515) tethrinoniculated-tethracross = E100(#^^##)^^#>#^#9

(6516) tethrideciculated-tethracross = E100(#^^##)^^#>#^#10

...

(6517) tethrispatialated-tethracross = E100(#^^##)^^#>#^#100

(6518) tethrideuterspatialated-tethracross = E100(#^^##)^^#>#^##100

(6519) tethritritospatialated-tethracross = E100(#^^##)^^#>#^###100

(6520) tethritetertospatialated-tethracross = E100(#^^##)^^#>#^####100

(6521) tethripeptospatialated-tethracross = E100(#^^##)^^#>#^#^#5

(6522) tethriextospatialated-tethracross = E100(#^^##)^^#>#^#^#6

(6523) tethrieptospatialated-tethracross = E100(#^^##)^^#>#^#^#7

(6524) tethriogdospatialated-tethracross = E100(#^^##)^^#>#^#^#8

(6525) tethrientospatialated-tethracross = E100(#^^##)^^#>#^#^#9

(6526) tethridekatospatialated-tethracross = E100(#^^##)^^#>#^#^#10

...

(6527) tethrisuperspatialated-tethracross = E100(#^^##)^^#>#^#^#100

(6528) tethriquadratetratediterated-tethracross = E100(#^^##)^^#>#^#^#^#100

(6529) tethriquintatetratediterated-tethracross = E100(#^^##)^^#>#^^#5

(6530) tethrisextatetratediterated-tethracross = E100(#^^##)^^#>#^^#6

(6531) tethriseptatetratediterated-tethracross = E100(#^^##)^^#>#^^#7

(6532) tethrioctatetratediterated-tethracross = E100(#^^##)^^#>#^^#8

(6533) tethrinonatetratediterated-tethracross = E100(#^^##)^^#>#^^#9

(6534) tethridecatetratediterated-tethracross = E100(#^^##)^^#>#^^#10

...

(6535) tethricentatetratediterated-tethracross = E100(#^^##)^^#>#^^#100

... here we reach the end at which this technique can be easily applied. Here I'll take a slight shift in gears to allow for better and more logical generalization...

(6536) tethrastaculated-tethritertethracross = E100(#^^##)^^#>#^^#100

(6537) territethrastaculated-tethritertethracross = E100(#^^##)^^#>(#^^#)^^#100

...

(6538) tethriterstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>#100

(6539) tethriditerstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>(#+#)100

(6540) tethritriterstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>(#+#+#)100

(6541) tethriquaditerstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>(#+#+#+#)100

...

(6542) tethrigriditerstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>##100

(6543) tethricubiterstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>###100

(6544) tethriquartiterstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>####100

...

(6545) tethrispatialiterstaculated-tethritertethracross = E100(#^^##)^^#>#^^#>#^#100

(6546) tethrisuperspatialiterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^#^#100

(6547) tethriquadratetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#4

(6548) tethriquintatetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#5

(6549) tethrisextatetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#6

(6550) tethriseptatetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#7

(6551) tethrioctatetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#8

(6552) tethrinonatetratediterstaculated-tethritertethracross

= E100(#^^##)^^#>#^^#>#^^#9

(6553) tethridecatetratediterstaculated-tethritertethracross 

= E100(#^^##)^^#>#^^#>#^^#10

...

(6554) dustaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^#>#^^#100

(6555) tristaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^#>#^^#>#^^#100

(6556) tetrastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##4

(6557) pentastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##5

(6558) sexastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##6

(6559) septastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##7

(6560) octastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##8

(6561) ennastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##9

(6562) dekastaculated-tethraturreted-tethritertethracross = E100(#^^##)^^#>#^^##10

...

(6563) tethracrossturreted-tethritertethracross = E100(#^^##)^^#>#^^##100

alternatively (6564) tethracross-turreted-tethritertethracross

with this we can also have...

(6565) deutero tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>#^^##*(#^^##)^^#>#^^##100

(6566) trito tethracross-turreted-tethritertethracross

= E100((#^^##)^^#>#^^##)^#3

(6567) teterto tethracross-turreted-tethritertethracross

= E100((#^^##)^^#>#^^##)^#4

...

even more insane we can have...

(6568) dutetrated tethracross-turreted-tethritertethracross

= E100((#^^##)^^#>#^^##)^((#^^##)^^#>#^^##)100

(6569) tritetrated tethracross-turreted-tethritertethracross

= E100((#^^##)^^#>#^^##)^^#3

(6570) quadratetrated tethracross-turreted-tethritertethracross

= E100((#^^##)^^#>#^^##)^^#4

...

(6571) terrible tethracrossturreted-tethritertethracross =

E100((#^^##)^^#>#^^##)^^#100

(6572) terrible terrible tethracrossturreted-tethritertethracross =

E100(((#^^##)^^#>#^^##)^^#)^^#100

...

(6573) hundred-ex-terrible tethracrossturreted-tethritertethracross 

E100(#^^##)^^#>(#^^##+#)100

...

(6574) godgahlah-teriterated-tethracruxiturreted-tethriterthethracross 

=E100(#^^##)^^#>(#^^##+#^#)100

(6575) tethrathoth-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+#^^#)100

(6576) terrible tethrathoth-teriterated-tethracruxiturreted-tethritertethracross

= E100((#^^##)^^#>(#^^##+#^^#))^^#100

(6577) hundred-ex-terrible tethrathoth-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+#^^#+#)100

(6578) Monster-Giant-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+(#^^#)^(#^^#)^#)100

(6579) territethrathoth-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+(#^^#)^^#)100

(6580) tethriterator-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+#^^#>#)100

(6581) dustaculated-tethrathoth-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+#^^#>#^^#)100

...

(6582) tethracross-teriterated-tethracruxiturreted-tethritertethracross

= E100(#^^##)^^#>(#^^##+#^^##)100

...

(6583) tethracross-by-hyperion-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#)100

(6584) tethracross-by-godgahlah-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#^#)100

(6585) tethracross-by-tethrathoth-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#^^#)100

(6586) tethracross-by-Monster-Giant-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*(#^^#)^(#^^#)^#)100

(6587) tethracross-by-territethrathoth-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*(#^^#)^^#)100

(6588) tethracross-by-tethriterator-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#^^#>#)100

(6589) tethracross-by-dustaculated-tethrathoth-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#^^#>#^^#)100

(6590) tethracross-by-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##*#^^##)100

(6591) tritified-tethracross-turreted-tethritertethracross 

= E100(#^^##)^^#>(#^^##*#^^##*#^^##)100

(6592) tetertified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#4

(6593) peptified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#5

(6594) extified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#6

(6595) eptified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#7

(6596) ogdified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#8

(6597) entified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#9

(6598) dekatified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#10

...

(6599) tethracruxifact-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^#100

...

(6600) tethracruxidutetrate-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^(#^^##)100

(6601) tethracruxitritetrate-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^(#^^##)^(#^^##)100

(6602) tethracruxiquadratetrate-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^(#^^##)^(#^^##)^(#^^##)100

= E100(#^^##)^^#>(#^^##)^^#4

...

(6603) territethracrossturreted-tethritertethracross = E100(#^^##)^^#>(#^^##)^^#100

                    ... you may notice how long and technical the names are getting. They are starting to sound more like chemical formulas, or taxonomy than numbers. The reason for this is the same reason why chemical names and taxonomy contain complicated names. When you start to have thousands of similar objects to name, you have to resort to longer names with interchangable parts to maintain clarity of meaning. xE^ allows for far greater freedom than previous ExE systems. There are many many many inbetween expressions between the obvious ones such as #^^##, #^^###, #^^#### etc. In fact we still have a long way to go to reach #^^###. We've only just begun with the ^^##-operator ...

(6604) tethritertethracrossturreted-tethritertethracross 

= E100(#^^##)^^#>(#^^##)^^#100

(also (6605) dustaculated-tethritertethracross)

 

(6606) duterritethracrossturreted-tethritertethracross 

= E100(#^^##)^^#>((#^^##)^^#)^^#100

...

(6607) hundred-ex-terrified-tethracross-turreted-tethritertethracross

= E100(#^^##)^^#>(#^^##)^^#>#100

...

(6608) tristaculated-tethritertethracross 

= E100(#^^##)^^#>(#^^##)^^#>(#^^##)^^#100

(6609) tetrastaculated-tethritertethracross

= E100(#^^##)^^##4

(6610) pentastaculated-tethritertethracross

E100(#^^##)^^##5

(6611) hexastaculated-tethritertethracross

= E100(#^^##)^^##6

(6612) heptastaculated-tethritertethracross

= E100(#^^##)^^##7

(6613) ogdastaculated-tethritertethracross

= E100(#^^##)^^##8

(6614) ennastaculated-tethritertethracross

= E100(#^^##)^^##9

(6615) dekastaculated-tethritertethracross

= E100(#^^##)^^##10

... and the nightmare continues ... and continues ... and continues ... and continues ...

(6616) secundotethrated-tethracross = E100(#^^##)^^##100

(6617) terrible secundotethrated-tethracross = E100((#^^##)^^##)^^#100

(6618) tethriterated-secundotethrated-tethracross = E100((#^^##)^^##)^^#>#100

(6619) dustaculated-secundotethrated-tethracross

E100((#^^##)^^##)^^#>((#^^##)^^##)^^#100

(6620) tristaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##3

(6621) quadrastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##4

(6622) quinquastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##5

(6623) sexastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##6

(6624) septastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##7

(6625) ogdastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##8

(6626) ennastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##9

(6627) dekastaculated-secundotethrated-tethracross

= E100((#^^##)^^##)^^##10

...

(6628) thrice-tethrasecunda = E100((#^^##)^^##)^^##100

(6629) quatrice-tethrasecunda = E100(((#^^##)^^##)^^##)^^##100

(6630) quincice-tethrasecunda = E100#^^##>#5

(6631) sextice-tethrasecunda = E100#^^##>#6

(6632) septice-tethrasecunda = E100#^^##>#7

(6633) octice-tethrasecunda = E100#^^##>#8

(6634) nonice-tethrasecunda = E100#^^##>#9

(6635) decice-tethrasecunda = E100#^^##>#10

...

Here we reach a familiar form ...

(6636) tethritercross = E100#^^##>#100

*formerly tethrasquared-iterator. Now defunct.

This is basically the same as a tethriterator, except that we are now iterating the 2nd tetrational operator, the tethrasecunda. With this in mind we can construct similar googolisms for the ^^##-operator, following the pattern of the iterated ^^#-operator...

(6637) tethriditercross = E100#^^##>(#+#)100

*formerly tethrasquared-du-iterator

(6638) tethritritercross = E100#^^##>(#+#+#)100

*formerly tethrasquared-triterator

(6639) tethriquaditercross = E100#^^##>(#+#+#+#)100

*formerly tethrasquared-quaditerator

(6640) tethriquiditercross = E100#^^##>##5

*formerly tethrasquared-quiditerator

(6641) tethrisiditercross = E100#^^##>##6

*formerly tethrasquared-siditerator

(6642) tethrisepitercross = E100#^^##>##7

*formerly tethrasquared-sepiterator

(6643) tethri-ogditercross = E100#^^##>##8

*formerly tethrasquared-ogditerator

(6644) tethrinonitercross = E100#^^##>##9

*formerly tethrasquared-noniterator

(6645) tethridecitercross = E100#^^##>##10

*formerly tethrasquared-deciterator

...

(6646) tethrigriditercross = E100#^^##>##100 

*formerly tethrasquared-griditerator

(6647) tethricubiculcross = E100#^^##>###100 

*formerly tethrasquared-cubiculator

(6648) tethriquarticulcross = E100#^^##>####100 

*formerly tethrasquared-quarticulator

(6649) tethriquinticulcross = E100#^^##>#^#5

*formerly tethrasquared-quinticulator

(6650) tethrisexticulcross = E100#^^##>#^#6

*formerly tethrasquared-sexticulator

(6651) tethrisepticulcross = E100#^^##>#^#7

*formerly tethrasquared-septiculator

(6652) tethri-octiculcross = E100#^^##>#^#8

*formerly tethrasquared-octiculator

(6653) tethrinoniculcross = E100#^^##>#^#9

*formerly tethrasquared-noniculator

(6654) tethrideciculcross = E100#^^##>#^#10

*formerly tethrasquared-deciculator

...

(6655) tethrispatialcross = E100#^^##>#^#100

*formerly tethrasquared-spatialator

... keep in mind we are now iterating the ^^##-operator using #^# diagonalization! So we are moving away from tethracross at an alarming rate. We still have further to go however to reach the first application of the ^^###-operator...

(6656) tethrisuperspatialcross= E100#^^##>#^#^#100

*formerly tethrasquared-superspatialator

(6657) tethritrimensionalcross = E100#^^##>#^#^#^#100

*formerly tethrasquared-quadratetratediterator

(6658) tethriquadramensionalcross = E100#^^##>#^^#5

*formerly tethrasquared-quintatetratediterator

(6659) tethriquintamensionalcross = E100#^^##>#^^#6

*formerly tethrasquared-sextatetratediterator

(6660) tethrisexamensionalcross = E100#^^##>#^^#7

*formerly tethrasquared-septatetratediterator

(6661) tethrseptamensionalcross = E100#^^##>#^^#8

*formerly tethrasquared-octatetratediterator

(6662) tethri-octamensionalcross = E100#^^##>#^^#9

*formerly tethrasquared-nonatetratediterator

(6663) tethrinonamensionalcross = E100#^^##>#^^#10

*formerly tethrasquared-decatetratediterator

(6664) tethraidecamensionalcross = E100#^^##>#^^#11

...

(6665) tethraturreted-tethracross = E100#^^##>#^^#100

(6666) dustacutethraturreted-tethracross = E100#^^##>#^^#>#^^#100

(6667) tristacutethraturreted-tethracross = E100#^^##>#^^#>#^^#>#^^#100

(6668) tetrastacutethraturreted-tethracross = E100#^^##>#^^##4

(6669) pentastacutethraturreted-tethracross = E100#^^##>#^^##5

(6670) hexastacutethraturreted-tethracross = E100#^^##>#^^##6

(6671) heptastacutethraturreted-tethracross = E100#^^##>#^^##7

(6672) ogdastacutethraturreted-tethracross = E100#^^##>#^^##8

(6673) ennastacutethraturreted-tethracross = E100#^^##>#^^##9

(6674) dekastacutethraturreted-tethracross = E100#^^##>#^^##10

...

(6675) dustaculated-tethracross = E100#^^##>#^^##100

(6676) terrible dustaculated-tethracross = E100(#^^##>#^^##)^^#100

(6677) tethriterated dustaculated-tethracross = E100(#^^##>#^^##)^^#>#100

(6678) terrisecunded dustaculated-tethracross = E100(#^^##>#^^##)^^##100

(6679) double terrisecunded dustaculated-tethracross 

= E100((#^^##>#^^##)^^##)^^##100

...

(6680) hundred-ex-terrisecunded dustaculated-tethracross = E100#^^##>(#^^##+#)100

...

(6681) tristaculated-tethracross = E100#^^##>#^^##>#^^##100

(6682) tetrastaculated-tethracross = E100#^^##>#^^##>#^^##>#^^##100

(6683) pentastaculated-tethracross = E100#^^###5

(6684) sexastaculated-tethracross = E100#^^###6

(6685) septastaculated-tethracross = E100#^^###7

(6686) ogdastaculated-tethracross = E100#^^###8

(6687) ennastaculated-tethracross = E100#^^###9

(6688) dekastaculated-tethracross = E100#^^###10

...

(6689) icosastaculated-tethracross = E100#^^###20

(6690) triantastaculated-tethracross = E100#^^###30

(6691) sarantastaculated-tethracross = E100#^^###40

(6692) penintastaculated-tethracross = E100#^^###50

(6693) exintastaculated-tethracross = E100#^^###60

(6694) ebdomintastaculated-tethracross = E100#^^###70

(6695) ogdontastaculated-tethracross = E100#^^###80

(6696) enenintastaculated-tethracross = E100#^^###90

...


Tethracubor Regiment

Category 62
Members: 276
(6697 - 6972)



 φ(3,0)



            Now we're getting somewhere. We now introduce the third tetrational operator , ^^###. This operator is referred to by the roots tethratertia, tethracubor, or territertiated...

 

(6697) tethracubor = E100#^^###100

also (6698) tethratertia

We have now reached an order of φ(3,0)

 

... once that is established there are plenty of constructions that follow, and some we can obtain with a little bit of tweaking ... here we go again ...

 

(6699) grand tethracubor = E100#^^###100#2 

(6700) grangol-carta-tethracubor = E100#^^###100#100 

(6701) grand grangol-carta-tethracubor = E100#^^###100#100#2

(6702) godgahlah-carta-tethracubor = E100#^^###100#^#100

(6703) tethrathoth-carta-tethracubor = E100#^^###100#^^#100

(6704) tethriterator-carta-tethracubor = E100#^^###100#^^#>#100

(6705) tethracross-carta-tethracubor = E100#^^###100#^^##100

 

...

 

(6706) tethracubor-by-deuteron= E100#^^###100#^^###100

 (6707) tethracubor-by-triton = E100#^^###100#^^###100#^^###100 

(6708) tethracubor-by-teterton = E100#^^###*#5

(6709) tethracubor-by-pepton = E100#^^###*#6

(6710) tethracubor-by-exton = E100#^^###*#7

(6711) tethracubor-by-epton = E100#^^###*#8

(6712) tethracubor-by-ogdon = E100#^^###*#9

(6713) tethracubor-by-enton = E100#^^###*#10

(6714) tethracubor-by-dekaton = E100#^^###*#11

... 

(6715) tethracubor-by-hecaton = E100#^^###*#101

...

(6716) tethracubor-by-hyperion = E100#^^###*#100

(6717) tethracubor-by-deutero-hyperion = E100#^^###*##100

(6718) tethracubor-by-trito-hyperion = E100#^^###*###100

(6719) tethracubor-by-teterto-hyperion = E100#^^###*####100

...

(6720) tethracubor-by-godgahlah = E100#^^###*#^#100

(6721) tethracubor-by-gridgahlah = E100#^^###*#^##100

(6722) tethracubor-by-godgathor = E100#^^###*#^#^#100

(6723) tethracubor-by-godtothol = E100#^^###*#^#^#^#100

...

(6724) tethracubor-by-tethrathoth = E100#^^###*#^^#100

(6725) tethracubor-by-Monster-Giant = E100#^^###*(#^^#)^(#^^#)^#100

(6726) tethracubor-by-terrible-tethrathoth = E100#^^###*(#^^#)^^#100

(6727) tethracubor-by-Behemoth-Giant = E100#^^###*(#^^#>2)^(#^^#>2)^#100

(6728) tethracubor-by-terrible-terrible-tethrathoth = E100#^^###*(#^^#>3)100

(6729) tethracubor-by-Trihemoth-Giant = E100#^^###*(#^^#>3)^(#^^#>3)^#100

...

(6730) tethracubor-by-tethriterator = E100#^^###*#^^#>#100

(6731) tethracubor-by-dustaculated-tethrathoth = E100#^^###*#^^#>#^^#100

...

(6732) tethracubor-by-tethracross = E100#^^###*#^^##100

(6733) tethracubor-by-tethritercross = E100#^^###*#^^##>#100

(6734) tethracubor-by-dustaculated-tethracross = E100#^^###*#^^##>#^^##100

...

(6735) deutero-tethracubor = E100#^^###*#^^###100

(6736) trito-tethracubor = E100#^^###*#^^###*#^^###100

(6737) teterto-tethracubor = E100#^^###*#^^###*#^^###*#^^###100 

(6738) pepto-tethracubor = E100(#^^###)^#5 

(6739) exto-tethracubor = E100(#^^###)^#6 

(6740) epto-tethracubor = E100(#^^###)^#7 

(6741) ogdo-tethracubor = E100(#^^###)^#8 

(6742) ento-tethracubor = E100(#^^###)^#9 

(6743) dekato-tethracubor = E100(#^^###)^#10 

...

(6744) isosto-tethracubor = E100(#^^###)^#20

(6745) trianto-tethracubor = E100(#^^###)^#30

(6746) saranto-tethracubor = E100(#^^###)^#40

(6747) peninto-tethracubor = E100(#^^###)^#50

(6748) exinto-tethracubor = E100(#^^###)^#60

(6749) ebdominto-tethracubor = E100(#^^###)^#70

(6750) ogdonto-tethracubor = E100(#^^###)^#80

(6751) eneninto-tethracubor = E100(#^^###)^#90

...

(6752) hecato-tethracubor = E100(#^^###)^#100

 

            here are some less immediate ones we can get with a little bit of modification from earlier googolism's ...

 

(6753) tethracuborfact = E100(#^^###)^#100 

(6754) grideutertethracubor = E100(#^^###)^##100 

(6755) kubicutethracubor = E100(#^^###)^###100 

(6756) quarticutethracubor = E100(#^^###)^####100 

(6757) quinticutethracubor = E100(#^^###)^#^#5 

(6758) sexticutethracubor = E100(#^^###)^#^#6 

(6759) septicutethracubor = E100(#^^###)^#^#7 

(6760) octicutethracubor = E100(#^^###)^#^#8

(6761) nonicutethracubor = E100(#^^###)^#^#9 

(6762) decicutethracubor = E100(#^^###)^#^#10

...

(6763) tethracuborgodgathored = E100(#^^###)^#^#100

(6764) tethracuborgralgathored = E100(#^^###)^#^##100 

... 

(6765) tethracuborgodtotholed = E100(#^^###)^#^#^#100

 

... here I'll introduce a new root operator. The ipso-operator takes the expression on the left and raises it to the power of the right (ips means to 'rise up' in greek)...

 

(6766) tethracubor-isptethrathoth = E100(#^^###)^#^^#100

(6767) tethracubor-isptethriterator = E100(#^^###)^#^^#>#100

(6768) tethracubor-isptethracross = E100(#^^###)^#^^##100 

(6769) tethracubor-isptethritercross = E100(#^^###)^#^^##>#100

(6770) tethracubor-isptethracubor = E100(#^^###)^(#^^###)100

(6771) Monster-Tethracubor = E100(#^^###)^(#^^###)^#100


... we'll also want to be able to tetrate hyperials ...


(6772) dutetrated-tethracubor = E100(#^^###)^(#^^###)100

 (6773) tritetrated-tethracubor = E100(#^^###)^(#^^###)^(#^^###)100 

(6774) quadratetrated-tethracubor = E100(#^^###)^^#4

(6775) quinquatetrated-tethracubor = E100(#^^###)^^#5

(6776) sexatetrated-tethracubor = E100(#^^###)^^#6

(6777) septatetrated-tethracubor = E100(#^^###)^^#7

(6778) octatetrated-tethracubor = E100(#^^###)^^#8

(6779) nonatetrated-tethracubor = E100(#^^###)^^#9

(6780) decatetrated-tethracubor = E100(#^^###)^^#10

...

(6781) vigintatetrated-tethracubor = E100(#^^###)^^#20

(6782) trigintatetrated-tethracubor = E100(#^^###)^^#30

(6783) quadragintatetrated-tethracubor = E100(#^^###)^^#40

(6784) quinquagintatetrated-tethracubor = E100(#^^###)^^#50

(6785) sexagintatetrated-tethracubor = E100(#^^###)^^#60

(6786) septuagintatetrated-tethracubor = E100(#^^###)^^#70

(6787) octogintatetrated-tethracubor = E100(#^^###)^^#80

(6788) nonagintatetrated-tethracubor = E100(#^^###)^^#90

...

(6789) terrible tethracubor = E100(#^^###)^^#100 

(6790) terrible terrible tethracubor = E100((#^^###)^^#)^^#100

 ...

(6791) hundred-ex-terrible tethracubor = E100(#^^###)^^#>#100 

 

... some further diagonalizations ...

 

(6792) tethriterated-tethracubor = E100(#^^###)^^#>#100

(6793) dustaculated-territethracubor = E100(#^^###)^^#>(#^^###)^^#100

(6794) tristaculated-territethracubor 

= E100(#^^###)^^#>(#^^###)^^#>(#^^###)^^#100 

(6795) tetrastaculated-territethracubor = E100(#^^###)^^##4 

(6796) pentastaculated-territethracubor = E100(#^^###)^^##5 

(6797) hexastaculated-territethracubor = E100(#^^###)^^##6

(6798) heptastaculated-territethracubor = E100(#^^###)^^##7

(6799) ogdastaculated-territethracubor = E100(#^^###)^^##8

(6800) ennastaculated-territethracubor = E100(#^^###)^^##9

(6801) dekastaculated-territethracubor = E100(#^^###)^^##10

...

 

(6802) icosastaculated-territethracubor = E100(#^^###)^^##20

(6803) triantastaculated-territethracubor = E100(#^^###)^^##30

(6804) sarantastaculated-territethracubor = E100(#^^###)^^##40

(6805) penintastaculated-territethracubor = E100(#^^###)^^##50

(6806) exintastaculated-territethracubor = E100(#^^###)^^##60

(6807) ebdomintastaculated-territethracubor = E100(#^^###)^^##70

(6808) ogdontastaculated-territethracubor = E100(#^^###)^^##80

(6809) enenintastaculated-territethracubor = E100(#^^###)^^##90

... 

(6810) hectastaculated-territethracubor = E100(#^^###)^^##100

 

... on a higher diagonalization ...

 

(6811) terrisquared-tethracubor = E100(#^^###)^^##100

(6812) terrible terrisquared-tethracubor = E100((#^^###)^^##)^^#100

 ...

(6813) territerated terrisquared-tethracubor = E100((#^^###)^^##)^^#>#100

(6814) double-terrisquared-tethracubor = E100((#^^###)^^##)^^##100 

(6815) triple-terrisquared-tethracubor = E100(((#^^###)^^##)^^##)^^##100 

(6816) quadruple-terrisquared-tethracubor = E100(#^^###)^^##>#4 

(6817) quintuple-terrisquared-tethracubor = E100(#^^###)^^##>#5

(6818) sextuple-terrisquared-tethracubor = E100(#^^###)^^##>#6 

(6819) septuple-terrisquared-tethracubor = E100(#^^###)^^##>#7

(6820) octuple-terrisquared-tethracubor = E100(#^^###)^^##>#8 

(6821) nonuple-terrisquared-tethracubor = E100(#^^###)^^##>#9 

(6822) decuple-terrisquared-tethracubor = E100(#^^###)^^##>#10

...

(6823) vigintuple-terrisquared-tethracubor = E100(#^^###)^^##>#20

(6824) trigintuple-terrisquared-tethracubor = E100(#^^###)^^##>#30

(6825) quadragintuple-terrisquared-tethracubor = E100(#^^###)^^##>#40

(6826) quinquagintuple-terrisquared-tethracubor = E100(#^^###)^^##>#50

(6827) sexagintuple-terrisquared-tethracubor = E100(#^^###)^^##>#60

(6828) septuagintuple-terrisquared-tethracubor = E100(#^^###)^^##>#70

(6829) octogintuple-terrisquared-tethracubor = E100(#^^###)^^##>#80

(6830) nonagintuple-terrisquared-tethracubor = E100(#^^###)^^##>#90

...

(6831) centuple-terrisquared-tethracubor = E100(#^^###)^^##>#100

 

... on a higher diagonalization ...

 

(6832) terrisquarediter-tethracubor = E100(#^^###)^^##>#100 

...

(6833) dustaculated-terrisquared-tethracubor 

= E100(#^^###)^^##>(#^^###)^^##100 

(6834) tristaculated-terrisquared-tethracubor = E100(#^^###)^^###3 

(6835) tetrastaculated-terrisquared-tethracubor = E100(#^^###)^^###4

(6836) pentastaculated-terrisquared-tethracubor = E100(#^^###)^^###5 

(6837) hexastaculated-terrisquared-tethracubor = E100(#^^###)^^###6 

(6838) heptastaculated-terrisquared-tethracubor = E100(#^^###)^^###7

(6839) ogdastaculated-terrisquared-tethracubor = E100(#^^###)^^###8

(6840) ennastaculated-terrisquared-tethracubor = E100(#^^###)^^###9

(6841) dekastaculated-terrisquared-tethracubor = E100(#^^###)^^###10

...

(6842) icosastaculated-terrisquared-tethracubor = E100(#^^###)^^###20

(6843) triantastaculated-terrisquared-tethracubor = E100(#^^###)^^###30

(6844) sarantastaculated-terrisquared-tethracubor = E100(#^^###)^^###40

(6845) penintastaculated-terrisquared-tethracubor = E100(#^^###)^^###50

(6846) exintastaculated-terrisquared-tethracubor = E100(#^^###)^^###60

(6847) ebdomintastaculated-terrisquared-tethracubor = E100(#^^###)^^###70

(6848) ogdontastaculated-terrisquared-tethracubor = E100(#^^###)^^###80

(6849) enenintastaculated-terrisquared-tethracubor = E100(#^^###)^^###90

...

(6850) hectastaculated-terrisquared-tethracubor = E100(#^^###)^^###100

 

... next level ...

 

(6851) tethraducubor = E100(#^^###)^^###100

(6852) terrible tethraducubor = E100((#^^###)^^###)^^#100

(6853) terrisquared-tethraducubor = E100((#^^###)^^###)^^##100

...

(6854) tethratricubor = E100((#^^###)^^###)^^###100

(6855) tethratetracubor = E100(((#^^###)^^###)^^###)^^###100 

(6856) tethrapentacubor = E100#^^###>#5

(6857) tethrahexacubor = E100#^^###>#6

(6858) tethraheptacubor = E100#^^###>#7

(6859) tethra-octacubor = E100#^^###>#8

(6860) tethra-ennacubor = E100#^^###>#9

(6861) tethradekacubor = E100#^^###>#10

(6862) tethra-endekacubor = E100#^^###>#11

(6863) tethra-dodekacubor = E100#^^###>#12

(6864) tethra-triadekacubor = E100#^^###>#13

(6865) tethra-tetradekacubor = E100#^^###>#14

(6866) tethra-pentadekacubor = E100#^^###>#15

(6867) tethra-hexadekacubor = E100#^^###>#16

(6868) tethra-heptadekacubor = E100#^^###>#17

(6869) tethra-octadekacubor = E100#^^###>#18

(6870) tethra-ennadekacubor = E100#^^###>#19

(6871) tethra-icosacubor = E100#^^###>#20

...

(6872) tethra-triantacubor = E100#^^###>#30

(6873) tethra-sarantacubor = E100#^^###>#40

(6874) tethra-penintacubor = E100#^^###>#50

(6875) tethra-exintacubor = E100#^^###>#60

(6876) tethra-ebdomintacubor = E100#^^###>#70

(6877) tethra-ogdontacubor = E100#^^###>#80

(6878) tethra-enenintacubor = E100#^^###>#90

...

(6879) tethrahectacubor = E100#^^###>#100

 

... and on to the next level ...

 

(6880) tethritercubor = E100#^^###>#100

alternatively (6881) tethracubiter

( not to be confused with tethricubiculator = E100#^^#>###100 )

(6882) tethriditercubor = E100#^^###>(#+#)100

alternatively (6883) tethracuborditerator

(6884) tethritritercubor = E100#^^###>(#+#+#)100

alternatively (6885) tethracubortriterator

(6886) tethriquaditercubor = E100#^^###>(#+#+#+#)100

 alternatively (6887) tethracuborquaditerator

(6888) tethriquiditercubor = E100#^^###>##5

 alternatively (6889) tethracuborquiditerator

(6890) tethrisiditercubor = E100#^^###>##6

 alternatively (6891) tethracuborsiditerator

(6892) tethrisepitercubor = E100#^^###>##7

 alternatively (6893) tethracuborseptiditerator

(6894) tethri-ogditercubor = E100#^^###>##8

 alternatively (6895) tethracuboroctiditerator

(6896) tethrinonitercubor = E100#^^###>##9

 alternatively (6897) tethracubornoniditerator

(6898) tethridecitercubor = E100#^^###>##10

 alternatively (6899) tethracubordeciditerator

...

(6900) tethrivigintitercubor = E100#^^###>##20

alternatively (6901) tethracuborvigintiditerator

(6902) tethritrigintitercubor = E100#^^###>##30

(6903) tethriquadragintitercubor = E100#^^###>##40

(6904) tethriquinquagintitercubor = E100#^^###>##50

(6905) tethrisexagintitercubor = E100#^^###>##60

(6906) tethriseptuagintitercubor = E100#^^###>##70

(6907) tethri-octogintitercubor = E100#^^###>##80

(6908) tethrinonagintitercubor = E100#^^###>##90

...

(6909) tethricentitercubor = E100#^^###>##100

alternatively (6910) tethracuborcentiditerator

 

... on a higher level ...

 

(6911) tethrigriditercubor = E100#^^###>##100

alternatively (6912) tethracubogridulator

(6913) tethricubiculcubor = E100#^^###>###100

 alternatively (6914) tethracubocubiculator

(6915) tethriquarticulcubor = E100#^^###>####100

 alternatively (6916) tethracuboquarticulator

(6917) tethriquinticulcubor = E100#^^###>#^#5

 alternatively (6918) tethracuboquinticulator

(6919) tethrisexticulcubor = E100#^^###>#^#6

 alternatively (6920) tethracubosexticulator

(6921) tethrisepticulcubor = E100#^^###>#^#7

 alternatively (6922) tethracubosepticulator

(6923) tethri-octiculcubor = E100#^^###>#^#8

 alternatively (6924) tethracubo-octiculator

(6925) tethrinoniculcubor = E100#^^###>#^#9

 alternatively (6926) tethracubononiculator

(6927) tethrideciculcubor = E100#^^###>#^#10

 alternatively (6928) tethracubodeciculator

... 

(6929) tethriviginticulcubor = E100#^^###>#^#20

alternatively (6930) tethracuboviginticulator

(6931) tethritriginticulcubor = E100#^^###>#^#30

(6932) tethriquadraginticulcubor = E100#^^###>#^#40

(6933) tethriquinquaginticulcubor = E100#^^###>#^#50

(6934) tethrisexaginticulcubor = E100#^^###>#^#60

(6935) tethriseptuaginticulcubor = E100#^^###>#^#70

(6936) tethri-octoginticulcubor = E100#^^###>#^#80

(6937) tethri-nonaginticulcubor = E100#^^###>#^#90

...

(6938) tethricenticulcubor = E100#^^###>#^#100

alternatively (6939) tethracubocenticulator

 

... on yet another level ...


(6940) gridgahlah-turreted-tethracubor = E100#^^###>#^##100

(6941) godgathor-turreted-tethracubor = E100#^^###>#^#^#100

(6942) godtothol-turreted-tethracubor = E100#^^###>#^#^#^#100

(6943) tethrathoth-turreted-tethracubor = E100#^^###>#^^#100

(6944) Monster-Giant-turreted-tethracubor = E100#^^###>(#^^#)^(#^^#)^#100

(6945) territethrathoth-turreted-tethracubor = E100#^^###>(#^^#)^^#100

(6946) Behemoth-Giant-turreted-tethracubor 

= E100#^^###>(#^^#>2)^(#^^#>2)^#100

(6947) territerritethrathoth-turreted-tethracubor = E100#^^###>((#^^#)^^#)^^#100

(6948) Trihemoth-Giant-turreted-tethracubor

= E100#^^###>(#^^#>3)^(#^^#>3)^#100

(6949) tethriterator-turreted-tethracubor = E100#^^###>#^^#>#100

(6950) dustacultethrathoth-turreted-tethracubor = E100#^^###>#^^#>#^^#100

(6951) tethracross-turreted-tethracubor = E100#^^###>#^^##100

(6952) tethritercross-turreted-tethracubor = E100#^^###>#^^##>#100

(6953) godgahlah-turreted-tethracross-turreted-tethracubor 

= E100#^^###>#^^##>#^#100

(6954) tethrathoth-turreted-tethracross-turreted-tethracubor

= E100#^^###>#^^##>#^^#100

(6955) dustacultethracross-turreted-tethracubor

= E100#^^###>#^^##>#^^##100

...

(6956) dustaculated-tethracubor = E100#^^###>#^^###100

(6957) tristaculated-tethracubor = E100#^^###>#^^###>#^^###100 

(6958) tetrastaculated-tethracubor = E100#^^###>#^^###>#^^###>#^^###100

(6959) pentastaculated-tethracubor = E100#^^####5

(6960) hexastaculated-tethracubor = E100#^^####6

(6961) heptastaculated-tethracubor = E100#^^####7

(6962) ogdastaculated-tethracubor = E100#^^####8

(6963) ennastaculated-tethracubor = E100#^^####9 

(6964) dekastaculated-tethracubor = E100#^^####10 

...

(6965) icosastaculated-tethracubor = E100#^^####20

(6966) triantastaculated-tethracubor = E100#^^####30

(6967) sarantastaculated-tethracubor = E100#^^####40

(6968) penintastaculated-tethracubor = E100#^^####50

(6969) exintastaculated-tethracubor = E100#^^####60

(6970) ebdomintastaculated-tethracubor = E100#^^####70

(6971) ogdontastaculated-tethracubor = E100#^^####80

(6972) enenintastaculated-tethracubor = E100#^^####90

...


 


Tethrateron Regiment

Category 63

Members: 246

(6973 - 7218)


 

φ(4,0)



                    

                    A 4-dimensional figure is popularly referred to as a polychoron. The term "polychoron" is derived from the greek roots "poly" (many) and "choros" (rooms). Hence the polychoron is literally composed of many closed 3-dimensional spaces referred to as polyhedrons. The implication here is that a "choron" on it's own is equivalent to a polyhedron. A 5-dimensional figure is referred to as a polyteron. Therefore a "teron" is a 4-dimensional figure equivalent to a polychoron.

 

                    Given the following we could either use tethrapolychoron or tethrateron, as the name for E100#^^####100. Here I've opted to use tethrateron because it's shorter and it ensures that the root "tera" meaning 4, matches up with the number of dimensions. If tethrapolychoron were used instead we would end up having an offset. 

 

        Tethrateron can be thought of as employing (in very loose terms mind you) a 4th dimensional power tower of hyperions. Namely it uses the delimiter #^^#4 which is equivalent to the notion of the ordinal w^^w4...

 

(6973) tethrateron = E100#^^####100

 

(from tethrathoth + teron)


alternatively (6974) tethratesseract

 We have now reached an order of φ(4,0)


                    Of coarse we can derive a whole family of googolism's based on extending (6975) tethraterror (E100#^^####100) using all the previously established constructions. Here is just a sampling...

 

(6976) grand tethrateron = E100#^^####100#2

...

(6977) grangol-carta-tethrateron = E100#^^####100#100

(6978) grand grangol-carta-tethrateron = E100#^^####100#100#2

...

(6979) godgahlah-carta-tethrateron = E100#^^####100#^#100

(6980) godgathor-carta-tethrateron = E100#^^####100#^#^#100

(6981) godtothol-carta-tethrateron = E100#^^####100#^#^#^#100

(6982) tethrathoth-carta-tethrateron = E100#^^####100#^^#100

(6983) Monster-Giant-carta-tethrateron = E100#^^####100(#^^#)^(#^^#)^#100

(6984) terrible-tethrathoth-carta-tethrateron = E100#^^####100(#^^#)^^#100

(6985) Behemoth-Giant-carta-tethrateron 

= E100#^^####100(#^^#>2)^(#^^#>2)^#100

(6986) terrible-terrible-tethrathoth-carta-tethrateron 

= E100#^^####100(#^^#>3)100

(6987) Trihemoth-Giant-carta-tethrateron

= E100#^^####100(#^^#>3)^(#^^#>3)^#100

(6988) tethriterator-carta-tethrateron

= E100#^^####100#^^#>#100

(6989) dustaculated-tethrathoth-carta-tethrateron

= E100#^^####100#^^#>#^^#100

(6990) tethracross-carta-tethrateron = E100#^^####100#^^##100

(6991) tethracubor-carta-tethrateron = E100#^^####100#^^###100

...

(6992) tethrateron-by-deuteron = E100#^^####100#^^####100

(6993) tethrateron-by-triton = E100#^^####100#^^####100#^^####100 

(6994) tethrateron-by-teterton = E100#^^####*#5

(6995) tethrateron-by-pepton = E100#^^####*#6

(6996) tethrateron-by-exton = E100#^^####*#7 

(6997) tethrateron-by-epton = E100#^^####*#8 

(6998) tethrateron-by-ogdon = E100#^^####*#9 

(6999) tethrateron-by-enton = E100#^^####*#10

(7000) tethrateron-by-dekaton = E100#^^####*#11

...

(7001) tethrateron-by-hyperion = E100#^^####*#100

(7002) tethrateron-by-godgahlah = E100#^^####*#^#100

(7003) tethrateron-by-godgathor = E100#^^####*#^#^#100

(7004) tethrateron-by-godtothol = E100#^^####*#^#^#^#100

(7005) tethrateron-by-tethrathoth = E100#^^####*#^^#100

(7006) tethrateron-by-Monster-Giant = E100#^^####*(#^^#)^(#^^#)^#100

(7007) tethrateron-by-terrible-tethrathoth = E100#^^####*(#^^#)^^#100

(7008) tethrateron-by-Behemoth-Giant = E100#^^####*(#^^#>2)^(#^^#>2)^#100

(7009) tethrateron-by-terrible-terrible-tethrathoth = E100#^^####*(#^^#>3)100

(7010) tethrateron-by-Trihemoth-Giant = E100#^^####*(#^^#>3)^(#^^#>3)^#100

(7011) tethrateron-by-tethriterator = E100#^^####*#^^#>#100

(7012) tethrateron-by-dustaculated-tethrathoth = E100#^^####*#^^#>#^^#100

(7013) tethrateron-by-tethracross = E100#^^####*#^^##100

(7014) tethrateron-by-tethracubor = E100#^^####*#^^###100

...

(7015) deutero-tethrateron = E100#^^####*#^^####100

 (7016) trito-tethrateron = E100#^^####*#^^####*#^^####100

(7017) teterto-tethrateron = E100(#^^####)^#4

(7018) pepto-tethrateron = E100(#^^####)^#5 

(7019) exto-tethrateron = E100(#^^####)^#6 

(7020) epto-tethrateron = E100(#^^####)^#7 

(7021) ogdo-tethrateron = E100(#^^####)^#8

(7022) ento-tethrateron = E100(#^^####)^#9

(7023) dekato-tethrateron = E100(#^^####)^#10

...

(7024) isosto-tethrateron = E100(#^^####)^#20

(7025) trianto-tethrateron = E100(#^^####)^#30

(7026) saranto-tethrateron = E100(#^^####)^#40

(7027) peninto-tethrateron = E100(#^^####)^#50

(7028) exinto-tethrateron = E100(#^^####)^#60

(7029) ebdominto-tethrateron = E100(#^^####)^#70

(7030) ogdonto-tethrateron = E100(#^^####)^#80

(7031) eneninto-tethrateron = E100(#^^####)^#90

...

(7032) tethrateronifact = E100(#^^####)^#100

(7033) grideutertethrateron = E100(#^^####)^##100

alternatively (7034) quadratatethrateron

(7035) kubicutethrateron = E100(#^^####)^###100 

(7036) quarticutethrateron = E100(#^^####)^####100 

(7037) quinticutethrateron = E100(#^^####)^#^#5

(7038) sexticutethrateron = E100(#^^####)^#^#6

(7039) septicutethrateron = E100(#^^####)^#^#7

(7040) octicutethrateron = E100(#^^####)^#^#8

(7041) nonicutethrateron = E100(#^^####)^#^#9

(7042) decicutethrateron = E100(#^^####)^#^#10

...

(7043) tethrateron-ad-godgahlah = E100(#^^####)^#^#100

(7044) tethrateron-ad-godgathor = E100(#^^####)^#^#^#100

(7045) tethrateron-ad-godtothol = E100(#^^####)^#^#^#^#100

(7046) tethrateron-ad-tethrathoth = E100(#^^####)^#^^#100

(7047) tethrateron-ad-Monster-Giant = E100(#^^####)^(#^^#)^(#^^#)^#100

(7048) tethrateron-ad-terrible-tethrathoth = E100(#^^####)^(#^^#)^^#100

(7049) tethrateron-ad-Behemoth-Giant = E100(#^^####)^(#^^#>2)^(#^^#>2)^#100

(7050) tethrateron-ad-terrible-terrible-tethrathoth = E100(#^^####)^(#^^#>3)100

(7051) tethrateron-ad-Trihemoth-Giant = E100(#^^####)^(#^^#>3)^(#^^#>3)^#100

(7052) tethrateron-ad-tethriterator = E100(#^^####)^#^^#>#100

(7053) tethrateron-ad-dustaculated-tethrathoth = E100(#^^####)^#^^#>#^^#100

(7054) tethrateron-ad-tethracross = E100(#^^####)^#^^##100

(7055) tethrateron-ad-tethracubor = E100(#^^####)^#^^###100

...

(7056) dutetrated-tethrateron = E100(#^^####)^(#^^####)100

(7057) tritetrated-tethrateron = E100(#^^####)^(#^^####)^(#^^####)100

(7058) quadratetrated-tethrateron = E100(#^^####)^^#4

(7059) quinquatetrated-tethrateron = E100(#^^####)^^#5

(7060) sexatetrated-tethrateron = E100(#^^####)^^#6

(7061) septatetrated-tethrateron = E100(#^^####)^^#7

(7062) octatetrated-tethrateron = E100(#^^####)^^#8

(7063) nonatetrated-tethrateron = E100(#^^####)^^#9

(7064) decatetrated-tethrateron = E100(#^^####)^^#10

...

(7065) terrible tethrateron = E100(#^^####)^^#100 

(7066) terrible terrible tethrateron = E100((#^^####)^^#)^^#100

(7067) three-ex-terrible tethrateron = E100(#^^####)^^#>#3

(7068) four-ex-terrible tethrateron = E100(#^^####)^^#>#4

(7069) five-ex-terrible tethrateron = E100(#^^####)^^#>#5

(7070) six-ex-terrible tethrathoth = E100(#^^####)^^#>#6

(7071) seven-ex-terrible tethrathoth = E100(#^^####)^^#>#7

(7072) eight-ex-terrible tethrathoth = E100(#^^####)^^#>#8

(7073) nine-ex-terrible tethrathoth = E100(#^^####)^^#>#9

(7074) ten-ex-terrible tethrathoth = E100(#^^####)^^#>#10

...

(7075) territerated-tethrateron = E100(#^^####)^^#>#100 

(7076) terriditerated-tethrateron = E100(#^^####)^^#>(#+#)100 

(7077) territriterated-tethrateron = E100(#^^####)^^#>(#+#+#)100 

...

(7078) terrigriditerated-tethrateron = E100(#^^####)^^#>##100

(7079) terricubiculated-tethrateron = E100(#^^####)^^#>###100

(7080) terriquarticulated-tethrateron = E100(#^^####)^^#>####100

...

(7081) godgahlah-turreted-territethrateron = E100(#^^####)^^#>#^#100

(7082) godgathor-turreted-territethrateron = E100(#^^####)^^#>#^#^#100

(7083) godtothol-turreted-territethrateron = E100(#^^####)^^#>#^#^#^#100

(7084) tethrathoth-turreted-territethrateron = E100(#^^####)^^#>#^^#100

(7085) Monster-Giant-turreted-territethrateron 

= E100(#^^####)^^#>(#^^#)^(#^^#)^#100

(7086) territethrathoth-turreted-territethrateron

= E100(#^^####)^^#>(#^^#)^^#100

(7087) Behemoth-Giant-turreted-territethrateron

= E100(#^^####)^^#>(#^^#>2)^(#^^#>2)^#100

(7088) territerritethrathoth-turreted-territethrateron

= E100(#^^####)^^#>(#^^#>3)100

(7089) Trihemoth-Giant-turreted-territethrateron

= E100(#^^####)^^#>(#^^#>3)^(#^^#>3)^#100

(7090) tethriterator-turreted-territethrateron

= E100(#^^####)^^#>#^^#>#100

(7091) dustacultethrathoth-turreted-territethrateron

= E100(#^^####)^^#>#^^#>#^^#100

(7092) tethracross-turreted-territethrateron

= E100(#^^####)^^#>#^^##100

(7093) tethracubor-turreted-territethrateron

= E100(#^^####)^^#>#^^###100

(7094) tethrateron-turreted-territethrateron

= E100(#^^####)^^#>#^^####100

...

(7095) dustaculated-territethrateron = E100(#^^####)^^#>(#^^####)^^#100 

(7096) tristaculated-territethrateron = E100(#^^####)^^##3

(7097) tetrastaculated-territethrateron = E100(#^^####)^^##4

 (7098) pentastaculated-territethrateron = E100(#^^####)^^##5

(7099) hexastaculated-territethrateron = E100(#^^####)^^##6

(7100) heptastaculated-territethrateron = E100(#^^####)^^##7

(7101) octastaculated-territethrateron = E100(#^^####)^^##8

(7102) ennastaculated-territethrateron = E100(#^^####)^^##9

(7103) dekastaculated-territethrateron = E100(#^^####)^^##10

...

(7104) terrisquared-tethrateron = E100(#^^####)^^##100

 (7105) terrible terrisquared-tethrateron = E100((#^^####)^^##)^^#100

(7106) dustaculated-terrible-terrisquared-tethrateron

= E100((#^^####)^^##)^^#>((#^^####)^^#)^^#100

 ...

(7107) double terrisquared-tethrateron = E100((#^^####)^^##)^^##100

(7108) terrible double terrisquared-tethrateron = E100(((#^^####)^^##)^^##)^^#100

(7109) dustaculated-terrible-double-terrisquared-tethrateron

= E100(((#^^####)^^##)^^##)^^##2

 ...

(7110) triple terrisquared-tethrateron 

= E100(((#^^####)^^##)^^##)^^##100

= E100(#^^####)^^##>#3

(7111) quadruple terrisquared-tethrateron = E100(#^^####)^^##>#4

(7112) quintuple terrisquared-tethrateron = E100(#^^####)^^##>#5

(7113) sextuple terrisquared-tethrateron = E100(#^^####)^^##>#6

(7114) septuple terrisquared-tethrateron = E100(#^^####)^^##>#7

(7115) octuple terrisquared-tethrateron = E100(#^^####)^^##>#8 

(7116) nonuple terrisquared-tethrateron = E100(#^^####)^^##>#9

(7117) decuple terrisquared-tethrateron = E100(#^^####)^^##>#10

... 

 (7118) centuple terrisquared-tethrateron = E100(#^^####)^^##>#100

(7119) godgahlah-turreted-terrisquared-tethrateron = E100(#^^####)^^##>#^#100

(7120) godgathor-turreted-terrisquared-tethrateron = E100(#^^####)^^##>#^#^#100

(7121) godtothol-turreted-terrisquared-tethrateron 

= E100(#^^####)^^##>#^#^#^#100

(7122) tethrathoth-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^#100

(7123) Monster-Giant-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>(#^^#)^(#^^#)^#100

(7124) territethrathoth-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>(#^^#)^^#100

(7125) tethriterator-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^#>#100

(7126) dustacultethrathoth-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^#>#^^#100

(7127) tethracross-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^##100

(7128) tethracubor-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^###100

(7129) tethrathoth-turreted-tethracross-turreted-tethracubor-turreted-terrisquared-tethrateron

E100(#^^####)^^##>#^^###>#^^##>#^^#100

@_@

(7130) tethrateron-turreted-terrisquared-tethrateron

= E100(#^^####)^^##>#^^####100

...

(7131) dustaculated-terrisquared-tethrateron 

= E100(#^^####)^^##>(#^^####)^^##100

(7132) tristaculated-terrisquared-tethrateron = E100(#^^####)^^###3

(7133) tetrastaculated-terrisquared-tethrateron = E100(#^^####)^^###4

(7134) pentastaculated-terrisquared-tethrateron = E100(#^^####)^^###5

(7135) hexastaculated-terrisquared-tethrateron = E100(#^^####)^^###6

(7136) heptastaculated-terrisquared-tethrateron = E100(#^^####)^^###7

(7137) octastaculated-terrisquared-tethrateron = E100(#^^####)^^###8

(7138) ennastaculated-terrisquared-tethrateron = E100(#^^####)^^###9

 (7139) dekastaculated-terrisquared-tethrateron = E100(#^^####)^^###10

...

(7140) terricubed-tethrateron = E100(#^^####)^^###100

(7141) double terricubed-tethrateron = E100((#^^####)^^###)^^###100

(7142) triple terricubed-tethrateron = E100(#^^####)^^###>#3

 (7143) quadruple terricubed-tethrateron = E100(#^^####)^^###>#4

(7144) quintuple terricubed-tethrateron = E100(#^^####)^^###>#5

(7145) sextuple terricubed-tethrateron = E100(#^^####)^^###>#6

(7146) septuple terricubed-tethrateron = E100(#^^####)^^###>#7

(7147) octuple terricubed-tethrateron = E100(#^^####)^^###>#8

(7148) nonuple terricubed-tethrateron = E100(#^^####)^^###>#9

(7149) decuple terricubed-tethrateron = E100(#^^####)^^###>#10

...

(7150) centuple terricubed-tethrateron = E100(#^^####)^^###>#100

(7151) godgahlah-turreted-terricubed-tethrateron = E100(#^^####)^^###>#^#100

(7152) godgathor-turreted-terricubed-tethrateron = E100(#^^####)^^###>#^#^#100

(7153) godtothol-turreted-terricubed-tethrateron = E100(#^^####)^^###>#^#^#^#100

(7154) tethrathoth-turreted-terricubed-tethrateron = E100(#^^####)^^###>#^^#100

(7155) Monster-Giant-turreted-terricubed-tethrateron

= E100(#^^####)^^##>(#^^#)^(#^^#)^#100

(7156) territethrathoth-turreted-terricubed-tethrateron

= E100(#^^####)^^##>(#^^#)^^#100

(7157) Behemoth-Giant-turreted-terricubed-tethrateron

= E100(#^^####)^^##>(#^^#>2)^(#^^#>2)^#100

(7158) territerritethrathoth-turreted-terricubed-tethrateron

= E100(#^^####)^^##>(#^^#>3)100

(7159) Trihemoth-Giant-turreted-terricubed-tethrateron

= E100(#^^####)^^##>(#^^#>3)^(#^^#>3)^#100

(7160) tethriterator-turreted-terricubed-tethrateron

= E100(#^^####)^^##>#^^#>#100

(7161) dustacultethrathoth-turreted-terricubed-tethrateron

= E100(#^^####)^^##>#^^#>#^^#100

(7162) tethracross-turreted-terricubed-tethrateron

= E100(#^^####)^^##>#^^##100

(7163) tethracubor-turreted-terricubed-tethrateron

= E100(#^^####)^^##>#^^###100

(7164) tethrateron-turreted-terricubed-tethrateron

= E100(#^^####)^^##>#^^####100

 ...

(7165) dustaculated-terricubed-tethrateron 

= E100(#^^####)^^###>(#^^####)^^###100

(7166) tristaculated-terricubed-tethrateron = E100(#^^####)^^####3 

(7167) tetrastaculated-terricubed-tethrateron = E100(#^^####)^^####4

(7168) pentastaculated-terricubed-tethrateron = E100(#^^####)^^####5

(7169) hexastaculated-terricubed-tethrateron = E100(#^^####)^^####6

(7170) heptastaculated-terricubed-tethrateron = E100(#^^####)^^####7

(7171) octastaculated-terricubed-tethrateron = E100(#^^####)^^####8

(7172) ennastaculated-terricubed-tethrateron = E100(#^^####)^^####9

(7173) dekastaculated-terricubed-tethrateron = E100(#^^####)^^####10

...

(7174) tethraduteron = E100(#^^####)^^####100 

(7175) tethratriteron = E100((#^^####)^^####)^^####100 

(7176) tethratetrateron = E100#^^####>#4 

(7177) tethrapentateron = E100#^^####>#5

(7178) tethrahexateron = E100#^^####>#6

(7179) tethraheptateron = E100#^^####>#7

(7180) tethra-octateron = E100#^^####>#8

(7181) tethra-ennateron = E100#^^####>#9

(7182) tethradekateron = E100#^^####>#10

(7183) tethra-endekateron = E100#^^####>#11

(7184) tethradodekateron = E100#^^####>#12

... 

(7185) tethra-icosateron = E100#^^####>#20

...

(7186) tethra-hectateron = E100#^^####>#100

alternatively (7187) tethriterteron

...

(7188) godgahlah-turreted-tethrateron = E100#^^####>#^#100

(7189) godgathor-turreted-tethrateron = E100#^^####>#^#^#100

(7190) godtothol-turreted-tethrateron = E100#^^####>#^#^#^#100

(7191) tethrathoth-turreted-tethrateron = E100#^^####>#^^#100

(7192) Monster-Giant-turreted-tethrateron = E100#^^####>(#^^#)^(#^^#)^#100

(7193) territethrathoth-turreted-tethrateron = E100#^^####>(#^^#)^^#100

(7194) Behemoth-Giant-turreted-tethrateron 

= E100#^^####>(#^^#>2)^(#^^#>2)^#100

(7195) territerritethrathoth-turreted-tethrateron

= E100#^^####>(#^^#>3)100

(7196) Trihemoth-Giant-turreted-tethrateron

= E100#^^####>(#^^#>3)^(#^^#>3)^#100

(7197) tethriterator-turreted-tethrateron = E100#^^####>#^^#>#100

(7198) dustacultethrathoth-turreted-tethrateron = E100#^^####>#^^#>#^^#100

(7199) tethracross-turreted-tethrateron = E100#^^####>#^^##100

(7200) tethracubor-turreted-tethrateron = E100#^^####>#^^###100

(7201) tethrathoth-turreted-tethracross-turreted-tethracubor-turreted-tethrateron

= E100#^^####>#^^###>#^^##>#^^#100

 ...

(7202) dustaculated-tethrateron = E100#^^####>#^^####100

(7203) tristaculated-tethrateron = E100#^^####>#^^####>#^^####100

(7204) tetrastaculated-tethrateron = E100#^^#####4

(7205) pentastaculated-tethrateron = E100#^^#####5

(7206) hexastaculated-tethrateron = E100#^^#####6

(7207) heptastaculated-tethrateron = E100#^^#####7

(7208) octastaculated-tethrateron = E100#^^#####8

(7209) ennastaculated-tethrateron = E100#^^#####9

(7210) dekastaculated-tethrateron = E100#^^#####10

...

(7211) icosastaculated-tethrateron = E100#^^#####20

(7212) triantastaculated-tethrateron = E100#^^#####30

(7213) sarantastaculated-tethrateron = E100#^^#####40

(7214) penintastaculated-tethrateron = E100#^^#####50

(7215) exintastaculated-tethrateron = E100#^^#####60

(7216) ebdomintastaculated-tethrateron = E100#^^#####70

(7217) ogdontastaculated-tethrateron = E100#^^#####80

(7218) enenintastaculated-tethrateron = E100#^^#####90

...



Tethrapeton Regiment

Category 64

Members: 181

(7219 - 7399)



φ(5,0)



 

                    ... as you can probably tell we have already settled into yet another regular pattern. I'll only give a smattering of googolism's possible for the next few groups. Keep in mind the pattern we've just established is still just the very beginning. We still just trying to get to the #^^#^# level, let alone to the pentational (#^^^#) level. We've still got a long way to go ...

 

(7219) tethrapeton = E100#^^#^#5 

(from tethrathoth + peton )

alternatively (7220) tethrapenteract

We have now reached an order of φ(5,0)


(7221) grand tethrapeton = E100#^^#5100#2

...

(7222) grangol-carta-tethrapeton = E100#^^#5100#100

(7223) grand grangol-carta-tethrapeton = E100#^^#^(5)100#100#2 

...

 (7224) godgahlah-carta-tethrapeton = E100#^^#^(5)100#^#100

(7225) tethrathoth-carta-tethrapeton = E100#^^#^(5)100#^^#100

(7226) Monster-Giant-carta-tethrapeton = E100#^^#^(5)100(#^^#)^(#^^#)^#100

(7227) territethrathoth-carta-tethrapeton = E100#^^#^(5)100(#^^#)^^#100

(7228) Behemoth-Giant-carta-tethrapeton 

= E100#^^#^(5)100(#^^#>2)^(#^^#>2)^#100

(7229) territerritethrathoth-carta-tethrapeton

= E100#^^#^(5)100(#^^#>3)100

(7230) Trihemoth-Giant-carta-tethrapeton

= E100#^^#^(5)100(#^^#>3)^(#^^#>3)^#100

(7231) tethriterator-carta-tethrapeton

= E100#^^#^(5)100#^^#>#100

(7232) dustacultethrathoth-carta-tethrapeton

= E100#^^#^(5)100#^^#>#^^#100

(7233) tethracross-carta-tethrapeton

= E100#^^#^(5)100#^^##100

(7234) tethracubor-carta-tethrapeton

= E100#^^#^(5)100#^^###100

(7235) tethrateron-carta-tethrapeton

= E100#^^#^(5)100#^^####100

(7236) tethrathoth-carta-tethracross-carta-tethracubor-carta-tethrateron-carta-tethrapeton

= E100#^^#^(5)100#^^####100#^^###100#^^##100#^^#100

...

(7237) tethrapeton-by-deuteron = E100#^^#5100#^^#5100

(7238) tethrapeton-by-triton = E100#^^#^(5)100#^^#^(5)100#^^#^(5)100

(7239) tethrapeton-by-teterton = E100#^^#^(5)*#5

(7240) tethrapeton-by-pepton = E100#^^#^(5)*#6

(7241) tethrapeton-by-exton = E100#^^#^(5)*#7

(7242) tethrapeton-by-epton = E100#^^#^(5)*#8

(7243) tethrapeton-by-ogdon = E100#^^#^(5)*#9

(7244) tethrapeton-by-enton = E100#^^#^(5)*#10

(7245) tethrapeton-by-dekaton = E100#^^#^(5)*#11

...

(7246) tethrapeton-by-hyperion = E100#^^#^(5)*#100

(7247) tethrapeton-by-godgahlah = E100#^^#^(5)*#^#100

(7248) tethrapeton-by-tethrathoth = E100#^^#^(5)*#^^#100

(7249) tethrapeton-by-Monster-Giant = E100#^^#^(5)*(#^^#)^(#^^#)^#100

(7250) tethrapeton-by-terrible-tethrathoth = E100#^^#^(5)*(#^^#)^^#100

(7251) tethrapeton-by-Behemoth-Giant = E100#^^#^(5)*(#^^#>2)^(#^^#>2)^#100

(7252) tethrapeton-by-terrible-terrible-tethrathoth = E100#^^#^(5)*(#^^#>3)100

(7253) tethrapeton-by-Trihemoth-Giant = E100#^^#^(5)*(#^^#>3)^(#^^#>3)^#100

(7254) tethrapeton-by-tethriterator = E100#^^#^(5)*#^^#>#100

(7255) tethrapeton-by-dustaculated-tethrathoth = E100#^^#^(5)*#^^#>#^^#100

(7256) tethrapeton-by-tethracross = E100#^^#^(5)*#^^##100

(7257) tethrapeton-by-tethracubor = E100#^^#^(5)*#^^###100

(7258) tethrapeton-by-tethrateron = E100#^^#^(5)*#^^####100

(7259) tethrapeton-by-tethrateron-by-tethracubor-by-tethracross-by-tethrathoth

= E100#^^#^(5)*#^^####*#^^###*#^^##*#^^#100

 ...

(7260) deutero-tethrapeton = E100#^^#5*#^^#5100

 (7261) trito-tethrapeton = E100#^^#^(5)*#^^#^(5)*#^^#^(5)100

(7262) teterto-tethrapeton = E100(#^^#^5)^#4

(7263) pepto-tethrapeton = E100(#^^#^5)^#5

(7264) exto-tethrapeton = E100(#^^#^5)^#6

(7265) epto-tethrapeton = E100(#^^#^5)^#7

(7266) ogdo-tethrapeton = E100(#^^#^5)^#8

(7267) ento-tethrapeton = E100(#^^#^5)^#9

(7268) dekato-tethrapeton = E100(#^^#^5)^#10

...

(7269) isosto-tethrapeton = E100(#^^#^5)^#20

(7270) trianto-tethrapeton = E100(#^^#^5)^#30

(7271) saranto-tethrapeton = E100(#^^#^5)^#40

(7272) peninto-tethrapeton = E100(#^^#^5)^#50

(7273) exinto-tethrapeton = E100(#^^#^5)^#60

(7274) ebdominto-tethrapeton = E100(#^^#^5)^#70

(7275) ogdonto-tethrapeton = E100(#^^#^5)^#80

(7276) eneninto-tethrapeton = E100(#^^#^5)^#90

 ...

(7277) tethrapetonifact = E100(#^^#5)^#100

(7278) quadratatethrapeton = E100(#^^#^5)^##100

(7279) kubikutethrapeton = E100(#^^#^5)^###100

(7280) quarticutethrapeton = E100(#^^#^5)^####100

(7281) quinticutethrapeton = E100(#^^#^5)^#^#5

(7282) sexticutethrapeton = E100(#^^#^5)^#^#6

(7283) septicutethrapeton = E100(#^^#^5)^#^#7

(7284) octicutethrapeton = E100(#^^#^5)^#^#8

(7285) nonicutethrapeton = E100(#^^#^5)^#^#9

(7286) decicutethrapeton = E100(#^^#^5)^#^#10

...

(7287) tethrapeton-ipso-godgahlah = E100(#^^#^5)^#^#100

(7288) tethrapeton-ipso-tethrathoth = E100(#^^#^5)^#^^#100

(7289) tethrapeton-ipso-Monster-Giant = E100(#^^#^5)^(#^^#)^(#^^#)^#100

(7290) tethrapeton-ipso-terrible-tethrathoth = E100(#^^#^5)^(#^^#)^^#100

(7291) tethrapeton-ipso-Behemoth-Giant = E100(#^^#^5)^(#^^#>2)^(#^^#>2)^#100

(7292) tethrapeton-ipso-terrible-terrible-tethrathoth = E100(#^^#^5)^(#^^#>3)100

(7293) tethrapeton-ipso-Trihemoth-Giant = E100(#^^#^5)^(#^^#>3)^(#^^#>3)^#100

(7294) tethrapeton-ipso-tethriterator = E100(#^^#^5)^#^^#>#100

(7295) tethrapeton-ipso-dustaculated-tethrathoth = E100(#^^#^5)^#^^#>#^^#100

(7296) tethrapeton-ipso-tethracross = E100(#^^#^5)^#^^##100

(7297) tethrapeton-ipso-tethracubor = E100(#^^#^5)^#^^###100

(7298) tethrapeton-ipso-tethrateron = E100(#^^#^5)^#^^####100

(7299) tethrapeton-ipso-tethrateron-ipso-tethracubor-ipso-tethracross-ipso-tethrathoth

= E100(#^^#^5)^(#^^####)^(#^^###)^(#^^##)^(#^^#)100

 ...

(7300) dutetrated-tethrapeton = E100(#^^#5)^(#^^#5)100

(7301) tritetrated-tethrapeton = E100(#^^#^5)^(#^^#^5)^(#^^#^5)100

(7302) quadratetrated-tethrapeton = E100(#^^#^5)^^#4

(7303) quintatetrated-tethrapeton = E100(#^^#^5)^^#5

(7304) sexatetrated-tethrapeton = E100(#^^#^5)^^#6

 (7305) septatetrated-tethrapeton = E100(#^^#^5)^^#7

(7306) octatetrated-tethrapeton = E100(#^^#^5)^^#8

(7307) nonatetrated-tethrapeton = E100(#^^#^5)^^#9

(7308) decatetrated-tethrapeton = E100(#^^#^5)^^#10

...

(7309) terrible tethrapeton = E100(#^^#5)^^#100

(7310) terrible terrible tethrapeton = E100((#^^#^5)^^#)^^#100

(7311) three-ex-terrible tethrapeton = E100(#^^#^5)^^#>#3

(7312) four-ex-terrible tethrapeton = E100(#^^#^5)^^#>#4

(7313) five-ex-terrible tethrapeton = E100(#^^#^5)^^#>#5

(7314) six-ex-terrible tethrapeton = E100(#^^#^5)^^#>#6

(7315) seven-ex-terrible tethrapeton = E100(#^^#^5)^^#>#7

(7316) eight-ex-terrible tethrapeton = E100(#^^#^5)^^#>#8

(7317) nine-ex-terrible tethrapeton = E100(#^^#^5)^^#>#9

(7318) ten-ex-terrible tethrapeton = E100(#^^#^5)^^#>#10

...

(7319) territerated tethrapeton = E100(#^^#5)^^#>#100

...

(7320) dustaculated-territethrapeton = E100(#^^#5)^^#>(#^^#5)^^#100

...

(7321) terrisquared-tethrapeton = E100(#^^#5)^^##100

(7322) two-ex-terrisquared-tethrapeton = E100((#^^#^5)^^##)^^##100

(7323) three-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(3)100

(7324) four-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(4)100

(7325) five-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(5)100

(7326) six-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(6)100

(7327) seven-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(7)100

(7328) eight-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(8)100

(7329) nine-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(9)100

(7330) ten-ex-terrisquared-tethrapeton = E100(#^^#^5)^^##>(10)100

 ...

(7331) tethritercrossed-tethrapeton = E100(#^^#^5)^^##>#100

(7332) dustaculated-terrisquared-tethrapeton = E100(#^^#^5)^^##>(#^^#^5)^^##100

... 

(7333) terricubed-tethrapeton = E100(#^^#5)^^###100

(7334) two-ex-terricubed-tethrapeton = E100((#^^#^5)^^###)^^###100

(7335) three-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(3)100

(7336) four-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(4)100

(7337) five-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(5)100

(7338) six-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(6)100

(7339) seven-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(7)100

(7340) eight-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(8)100

(7341) nine-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(9)100

(7342) ten-ex-terricubed-tethrapeton = E100(#^^#^5)^^###>(10)100

...

(7343) tethritercubed-tethrapeton = E100(#^^#^5)^^###>#100

(7344) dustaculated-terricubed-tethrapeton 

= E100(#^^#^5)^^###>(#^^#^5)^^###100

 ...

(7345) territesserated-tethrapeton = E100(#^^#5)^^####100

(7346) two-ex-territesserated-tethrapeton = E100((#^^#^5)^^####)^^####100

(7347) three-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(3)100

(7348) four-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(4)100

(7349) five-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(5)100

(7350) six-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(6)100

(7351) seven-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(7)100

(7352) eight-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(8)100

(7353) nine-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(9)100

(7354) ten-ex-territesserated-tethrapeton = E100(#^^#^5)^^####>(10)100

 ...

(7355) tethritertesserated-tethrapeton = E100(#^^#^5)^^####>#100

(7356) dustaculated-territesserated-tethrapeton 

= E100(#^^#^5)^^####>(#^^#^5)^^####100

...

(7357) tethradupeton = E100(#^^#5)^^#5100

(7358) tethratripeton = E100((#^^#5)^^#5)^^#5100

(7359) tethratetrapeton = E100(((#^^#5)^^#5)^^#5)^^#5100

(7360) tethrapentapeton = E100#^^#5>#5

(7361) tethrahexapeton = E100#^^(#^5)>#6

(7362) tethraheptapeton = E100#^^(#^5)>#7

(7363) tethra-octapeton = E100#^^(#^5)>#8

(7364) tethra-ennapeton = E100#^^(#^5)>#9

(7365) tethradekapeton = E100#^^(#^5)>#10

(7366) tethra-endekapeton = E100#^^(#^5)>#11

(7367) tethradodekapeton = E100#^^(#^5)>#12

 ...

(7368) tethra-icosapeton = E100#^^(#^5)>#20

...

 

(7369) tethriterpeton = E100#^^#5>#100

 (7370) godgahlah-turreted-tethrapeton = E100#^^(#^5)>#^#100

(7371) tethrathoth-turreted-tethrapeton = E100#^^(#^5)>#^^#100

(7372) Monster-Giant-turreted-tethrapeton = E100#^^(#^5)>(#^^#)^(#^^#)^#100

(7373) territethrathoth-turreted-tethrapeton = E100#^^(#^5)>(#^^#)^^#100

(7374) Behemoth-Giant-turreted-tethrapeton 

= E100#^^(#^5)>(#^^#>2)^(#^^#>2)^#100

(7375) territerritethrathoth-turreted-tethrapeton

= E100#^^(#^5)>(#^^#>3)100

(7376) Trihemoth-Giant-turreted-tethrapeton

= E100#^^(#^5)>(#^^#>3)^(#^^#>3)^#100

(7377) tethriterator-turreted-tethrapeton

= E100#^^(#^5)>#^^#>#100

(7378) dustacultethrathoth-turreted-tethrapeton

= E100#^^(#^5)>#^^#>#^^#100

(7379) tethracross-turreted-tethrapeton

= E100#^^(#^5)>#^^##100

(7380) tethracubor-turreted-tethrapeton

= E100#^^(#^5)>#^^###100

(7381) tethrateron-turreted-tethrapeton

= E100#^^(#^5)>#^^####100

(7382) tethrathoth-turreted-tethracross-turreted-tethracubor-turreted-tethrateron-turreted-tethrapeton

= E100#^^(#^5)>#^^####>#^^###>#^^##>#^^#100

... 

(7383) dustaculated-tethrapeton = E100#^^#5>#^^#5100

(7384) tristaculated-tethrapeton = E100#^^#5>#^^#5>#^^#5100

(7385) tetrastaculated-tethrapeton = E100#^^#5>#^^#5>#^^#5>#^^#5100

 (7386) pentastaculated-tethrapeton = E100#^^#^(6)5

(7387) hexastaculated-tethrapeton = E100#^^#^(6)6

(7388) heptastaculated-tethrapeton = E100#^^#^(6)7

(7389) octastaculated-tethrapeton = E100#^^#^(6)8

(7390) ennastaculated-tethrapeton = E100#^^#^(6)9

(7391) dekastaculated-tethrapeton = E100#^^#^(6)10

...

(7392) icosastaculated-tethrapeton = E100#^^#^(6)20

(7393) triantastaculated-tethrapeton = E100#^^#^(6)30

(7394) sarantastaculated-tethrapeton = E100#^^#^(6)40

(7395) penintastaculated-tethrapeton = E100#^^#^(6)50

(7396) exintastaculated-tethrapeton = E100#^^#^(6)60

(7397) ebdomintastaculated-tethrapeton = E100#^^#^(6)70

(7398) ogdontastaculated-tethrapeton = E100#^^#^(6)80

(7399) enenintastaculated-tethrapeton = E100#^^#^(6)90

...




Continue to Part II for numbers on the order of φ(6,0) to φ(10,0)