ULNL3

Back to Ultimate Large Numbers List Part II

ULTIMATE LARGE NUMBERS LIST

PART III

Cascading-E, Extended Cascading-E & Beyond

numbers of order type w^w to any number below infinity...

E100#^#100

E100### ... ###100 w/100 #s

godgahlah

                This number pushes the limit of xE#, and soon we will be beyond what we can practically expression even in xE#. However this is just the beginning of Cascading-E Notation. In Cascading-E we can write a godgahlahmore simply as E100#^#100. This number can be approximated in Array Notation as <10,100,99,99,...,99> w/99 99s. This makes it an array with 101 entries. On googology wiki this number is approximated as <100,101(1)2> which is <100,100,...,100> w/101 100s. 

E100,000#### ... ... ####100,000 w/100,000 #s

godgahlahgong

            Also can be written in cascading-E as E100,000#^#100,000.

{10, {10,10(1)2} (1)2}

iteralplex

The plex version of an iteral. This is one of the 120 original named numbers by Jonathan Bowers.

E100#^#100#2

E100######## ... ... ... ... ... ... ... ... ... ... ... ... ########100 

w/godgahlah #s

grand godgahlah

            Also can be written E100#^#100#2 = E100#^#(E100#^#100) = E100#^#godgahlah

E100,000######## ... ... ... ... ... ... ... ... ... ... ... ... ########100,000 w/godgahlahgong #s

grand godgahlahgong

            Alternatively, E100,000#^#100,000#2.

E100#grand godgahlah100

grand grand godgahlah

            This is E100#^#100#3 in Cascading-E. We can also called this number two-ex-grand godgahlah, although this doesn't really shorten the name.

E100,000#grand godgahlahgong100,000

grand grand godgahlahgong

                This is E100,000#^#100,000#3. This was the highest official entry with the original release of my Ultimate Large Numbers List. That being said someone out there probably suggested ...

1+E100,000#^#100,000#3

grand grand godgahlahgong and one

                In an earlier version of this list, this number was mentioned unofficially (non-entry) as an example of the first really large number on the way to infinity. Adding one to googolism's is a common knee-jerk response from non-googologist's. By mentioning such a number, non-googologist's imply that "there is no largest number" and therefore there is no point in trying to make one. By claiming that they have "named the largest number by adding one" they hope to lampoon the endeavor entirely.

                What they fail to realize is that googologist's are not trying to make the "largest number", but rather simply enjoy making extremely large numbers, and competing with fellow googologist's in this effort. Secondly, there is a big difference from adding one to someone else's googolism and building your own from the ground up. This is equivalent to "standing on the shoulders of giants" in the worst possible sense. There is generally a "gentlemen's agreement" in googology which says you should not make reference to the other person's number in your definition in an attempt to "trump" them, since any number can be trivially made larger by adding one to it (including some infinities I might add). The second rule is you don't get bragging rights if your number is constructable with methods already established by a competitor. In a sense, adding one contributes nothing to the discussion of large numbers. The idea isn't just to make the largest number, but also to keep devising new and better ways to generate large numbers. So it is a misconception that googologist's are only trying to find the largest number. Rather googologist's are always trying to find a larger number, and not just a slightly larger number, but a colossally mind-bogglingly crushing SUPER ULTRA MEGA NE PLUS ULTRA Larger Number ... and that just for a warm up... 

2+E100,000#^#100,000#3

grand grand godgahlahgong and two

            because for every googolism, there will be a +1er to add one to it. See (grand grand godgahlahgong and one). Moving on...

2E100,000#^#100,000#3

two grand grand godgahlahgong

            This is a step up from the +1ers, as we are now adding a grand grand godgahlahgong to a grand grand godgahlahgong. We can truncate this as two times a grand grand godgahlahgong. Since our ordinary number sense is logarithmic however, this isn't really an impressive improvement. If the grand grand godgahlahgong is represented by a solid packed sphere of fundamental particles, two grand grand godgahlahgong, would be like having two of these spheres. Does it really seem that much larger, no matter how large the original number was?

3E100,000#^#100,000#3

three grand grand godgahlahgong

            How about 3 times a grand grand godgahlahgong...

7E100,000#^#100,000#3

seven grand grand godgahlahgong

            How about 7 times a grand grand godgahlahgong...

(E100,000#^#100,000#3)^2

grand grand godgahlahgong squared

            This is the next stage in the naive non-googologist's attempt to extend a target googolism. Basically an attempt to pre-empt the impulse to say "two times your number" and jump to "your number times your number". Now you can imagine our sphere of particles compare to a grand grand godgahlahgong of such spheres!!! o_0;

            This will tend to get a visceral reaction, especially since we can't even imagine how big this number is. Despite that fact however, this is just squaring, so any grade school kid could come up with that. Furthermore try to remember that if we began by looking at a single fundamental particle and zoomed out until we reached a grand grand godgahlahgong particles, we'd only have to zoom out twice as long to reach a grand grand godgahlahgong squared. Given how mind-crushingly long the zoom out would be, the fact that it would take twice as long barely makes a difference. Hence, from a googological point of view there is virtually no difference between these numbers. Moving on...

(E100,000#^#100,000#3)^3

grand grand godgahlahgong cubed

            What's better than a square ... a cube...

(E100,000#^#100,000#3)^4

grand grand godgahlahgong to the fourth

            or a 4th power ...

(E100,000#^#100,000#3)^(E100,000#^#100,000#3)

grand grand godgahlahgong to the power of itself

            Next up along the hierarchy of naive responses is raising the number to its own power. Again, with numbers this large it has virtually no effect. That probably sounds mind boggling but just imagine N, then N^N, then (N^N)^(N^N), and continue in this manner for N steps, and call this number M. Someone comes along and says "I could trounce M, how about M^M". Are you really going to be impressed by their response? Ditto for googologist's who've gone much much further ...

(E100,000#^#100,000#3)^^(E100,000#^#100,000#3)

power tower of grand grand godgahlahgong's a grand grand godgahlah terms high

            This one is a classic. Even non-googologist's eventually realize that simply raising a number to the power of itself isn't really that competitive for certain large numbers, especially after they have at least been exposed toGraham's Number. So next they decide to create a power tower of this number, naively thinking this will trounce the competition. But for anything above Graham's Number this already has virtually no effect. If "N" is any googolism, you can bet someone out there will mention N^^N as a response. Rule 34 of googolism states: "If a googolism exists, there is a salad number for it, ... no exceptions". Moving on...

(E100,000#^#100,000#3)^^^^^ ... ^^^^^^(E100,000#^#100,000#3)

w/(E100,000#^#100,000#3) ^s

            Time to bring out the big guns. Our intrepid non-googologist has now gotten wind of Knuth-up arrow notation. They promptly take N and generate N^^^...^^^N w/N ^s. As any googologist worth his/her salt knows, no matter how amazingly powerful a "method" is in ordinary terms, it will always be obsolete moments later. The general rule of thumb is, never use a method that occurred earlier in the game to extend a number late in the game. It's effect will always be negligible relative to the current methods. Even the next entry is vastly larger despite making only a minute change...

E100,000#^#(1+E100,000#^#100,000#2)

            So the non-googologist actually realizes that they can't use any methods other than the most recently established one. Great. Now they attempt to apply that principle and ... miss the point. Since a grand grand godgahlahgong is E100,000####...####100,000 with a grand godgahlahgong #s, a naive response might be to have E100,000####...#####100,000 with a grand godgahlahgong +1 #s. This isn't much of an improvement over just adding one to the number! This response however is still mind-bogglingly better than the last attempt.

 To prove this just consider the following. Let n=grand godgahlahgong, and N=grand grand godgahlahgong.By definition N = E100,000#^(n)100,000. We first observe that:

E100,000#^(n+1)100,000 > E100,000#^(n+1)3 = E100,000#^(n)100,000#^(n)100,000 

> E100,000#^(n)100,000#100,000 > E100,000#^(n)100,000#2 

= E100,000#^(n)(E100,000#^(n)100,000) = E100,000#^(n)N

                Next we work from the other end. We can say that:

<N,N,N> < E(N)N##N < E100,000##(N+1) = E100,000##100,000#N <

E100,000###N < E100,000#^(n)N 

So we conclude...

<grand grand godgahlahgong,3(1)2> < E100,000#^(grand godgahlahgong+1)100,000

E100,000#^#100,000#4

grand grand grand godgahlahgong

            This is the obvious response to a grand grand godgahlahgong. This number is mind-bogglingly more massive. However, just like all the previous attempts to extend a grand grand godgahlahgong this is still too tame an extension, because it employs a method we have been using since the beginning: basic recursion. At this point, the recursion is so complex that applying one additional recursion doesn't make much of a difference from a googologist's point of view. Okay so how about...

E100,000#^#100,000#5

grand grand grand grand godgahlahgong

                Same problem as before. Still just basic recursion... how about ...

E100#^#100#100

grandgahlah

                This is the smallest new number defined with Cascading-E Notation. A grandgahlah may also be called a grand grand grand ... grand grand grand godgahlah where there are 99 grands. For this we can use the short hand name ninety-nine-ex-grand godgahlah. This still isn't a significant improvement from agodgahlah since we already introduced proto-hyperions a long time ago.

E100#^#100#101

hundred-ex-grand godgahlah

                Trivial, but it just sounds cool...

E100,000#^#100,000#11,863

            grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand 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grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand 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grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand grand godgahlahgong 

            Also known as eleven-thousand-eight-hundred-sixty-two-ex-grand godgahlahgong. Just kidding. This is a number based on the original trail of grands I had left at the end of my ULNL with it's initial release to suggest the next direction of development. Obviously, listing out the grands is inefficient. Still it's mind-boggling to think how all these "grand"s modify "godgahlahgong". Even so, this kind of stuff is easily trumped by the many numbers that follow as we begin to explore the consequences of Cascading-E notation... 

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

godgahlah-ex-grand godgahlah

            This response is far far better than any of the previous responses... but it's still a naive extension. Why? Because it still only requires a single extra proto-hyperion to achieve these results, and with two proto-hyperions we get even further.

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

grand-godgahlah-ex-grand godgahlah

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

grand-grand-godgahlah-ex-grand godgahlah

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

grand-grand-grand-godgahlah-ex-grand godgahlah

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

grand-grand-grand-grand-godgahlah-ex-grand godgahlah

E100#^#100#100#2

grand grandgahlah

                E100#^#100#100#2 = E100#^#100#(E100#^#100#100) = E100#^#100#(grandgahlah). The great grandgahlah is the grandgahlahth member of the godgahlah series.

E100#^#100#100#3

grand grand grandgahlah

E100#^#100#100#100

greagahlah

E100#^#100#100#100#2

grand greagahlah

E100#^#100#100#100#3

grand grand greagahlah

E100#^#100#100#100#100

gigangahlah

E100#^#100#100#100#100#2

grand gigangahlah

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

gorgegahlah

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

gulgahlah

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

gaspgahlah

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

ginorgahlah

E100#^#100##100

gugoldgahlah

E100#^#100##100#100

graatagoldgahlah

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

greegoldgahlah

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

grinningoldgahlah

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

golaagoldgahlah

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

gruelohgoldgahlah

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

gaspgoldgahlah

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

ginorgoldgahlah

E100#^#100##100##100

gugolthragahlah

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

gugolteslagahlah

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

gugolpetagahlah

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

gugolhexagahlah

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

gugolheptagahlah

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

gugoloctagahlah

E100#^#100###100

throogahlah

E100#^#100####100

teroogahlah

E100#^#100#####100

petoogahlah

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

ectoogahlah

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

zettoogahlah

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

yottoogahlah

E100#^#100#^#100

gotrigahlah / tristo-godgahlah

E100#^#100#^#100#2

grand gotrigahlah

E100#^#100#^#100#3

grand grand gotrigahlah

E100#^#100#^#100#100

grantrigahlah

E100#^#100#^#100#100#2

great grantrigahlah

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

greatrigahlah

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

gigantrigahlah

E100#^#100#^#100##5

gorgetrigahlah

E100#^#100#^#100##6

gultrigahlah

E100#^#100#^#100##7

gasptrigahlah

E100#^#100#^#100##8

ginortrigahlah

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

gugoldtrigahlah

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

throotrigahlah

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

terootrigahlah

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

petootrigahlah

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

ectootrigahlah

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

zettootrigahlah

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

yottootrigahlah

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

gotergahlah / teristo-godgahlah

E100#^#100#^#100#^#100#2

grand gotergahlah

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

grantergahlah

E100#^#100#^#100#^#100#100#2

grand grantergahlah

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

greatergahlah

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

gigantergahlah

E100#^#100#^#100#^#100##5

gorgetergahlah

E100#^#100#^#100#^#100##6

gultergahlah

E100#^#100#^#100#^#100##7

gasptergahlah

E100#^#100#^#100#^#100##8

ginortergahlah

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

throotergahlah

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

terootergahlah

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

petootergahlah

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

ectootergahlah

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

zettootergahlah

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

yottootergahlah

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

gopeggahlah / pesto-godgahlah

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

gohexgahlah / existo-godgahlah

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

gohepgahlah / episto-godgahlah

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

go-ahtgahlah / ogisto-godgahlah

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

go-enngahlah / ennisto-godgahlah

{10,10(1)10}

emperal

The emperal was one of the original 120 named numbers by Jonathan Bowers. It falls slightly below a godekahlah. An emperal may be expanded to: 

{10,10,10,10,10,10,10,10,10,10(1)9}

<10,100(1)10>

This is a proposed lowerbound for godekahlah in BEAF. If this bound is true, then it is trivially larger than an emperal. This number expands to <10,10,...,10(1)9> w/100 10s.

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

godekahlah / dekisto-godgahlah

E100#^#*#100

godgoldgahlah

A godgoldgahlah is approximately equal to <10,100(1)100>.

{10,10 (1) {10,10 (1) 10}}

emperalplex

The plex version of an emperal. This would be approximately E100#^#*#emperal in Cascading-E Notation. Since an emperal is itself approximately E100#^#*#10 this means this number can be approximated as E100#^#*#10#2. Clearly this is smaller than 100#^#*#100#2, which is vanishingly small compare to the next entry ...

E100#^#*#100#^#*#100

gotrigoldgahlah / tristo-godgoldgahlah

Approximately equal <10,100(1)100,2> 

E100#^#*#100#^#*#100#^#*#100

gotergoldgahlah / teristo-godgoldgahlah

Approximately equal <10,100(1)100,3>

E100#^#*##5

gopeggoldgahlah / pesto-godgoldgahlah

Approximately equal <10,100(1)100,4>

E100#^#*##6

gohexgoldgahlah / existo-godgoldgahlah

Approximately equal <10,100(1)100,5>

E100#^#*##7

gohepgoldgahlah / episto-godgoldgahlah

Approximately equal <10,100(1)100,6>

E100#^#*##8

go-ahtgoldgahlah / ogisto-godgoldgahlah

Approximately equal <10,100(1)100,7>

E100#^#*##9

godenngoldgahlah / ennisto-godgoldgahlah

Approximately equal <10,100(1)100,8>

E100#^#*##10

godekagoldgahlah / dekisto-godgoldgahlah

Approximately equal <10,100(1)100,9>

{10,10(1)10,10}

hyperal

One of the original Bowerisms. It is believed to fall between E100#^#*##10 and E100#^#*##11.

E100#^#*##100

godthroogahlah

Approximately equal <10,100(1)100,99>

{ 10 , 10 (1) 10 , { 10 , 10 (1) 10 , 10 } }

hyperalplex

This is bigger than a godthroogahlah but less than a grand godthroogahlah.

E100#^#*###100

godteroogahlah

Approximately equal <10,100(1)100,99,99>

E100#^#*####100

godpetoogahlah

Approximately equal <10,100(1)100,99,99,99>

E100#^#*#####100

go-ectoogahlah

Approximately equal <10,100(1)100,99,99,99,99>

E100#^#*######100

godzettoogahlah

Approximately equal <10,100(1)100,99,99,99,99>

E100#^#*#######100

godyottoogahlah

Approximately equal <10,100(1)100,99,99,99,99,99>

E100#^#*#^#100

deutero-godgahlah

This is the first number to introduce the "deutero" operator. This duplicates the hypernion, leading to two copies multiplied together. This is believed to be approximately equal to <10,100(1)(1)2>. That is a two-row array equal to <10,10,...,10(1)10,10,...,10> w/100 10s per row. This makes this number much much larger than a hyperal. This number is still much much smaller than a dutridecal.

E100#^#*#^#*#100

deutero-godgoldgahlah

Approximately equal to <10,100(1)(1)100>

E100#^#*#^#*##100

deutero-godthroogahlah

Approximately equal to <10,100(1)(1)100,99>

{3,3,3(1)3,3,3(1)3,3,3}

dutritri

One of Bowers' originals.

{10,10,10(1)10,10,10(1)10,10,10}

dutridecal

One of Bowers' originals. 

E100#^#*#^#*###100

deutero-godteroogahlah

Approximately equal to <10,100(1)(1)100,99,99>

E100#^#*#^#*####100

deutero-godpetoogahlah

E100#^#*#^#*#####100

deutero-go-ectoogahlah

E100#^#*#^#*######100

deutero-gozettoogahlah

E100#^#*#^#*#######100

deutero-goyottoogahlah

E100#^#*#^#*#^#100

trito-godgahlah

Approximately equal to <10,100(1)(1)(1)2>. Thats <100&10 (1) 100&10 (1) 100&10 > or three rows of a hundred 10s. This number exceeds a dutridecal.

E100#^#*#^#*#^#*#^#100

teterto-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)2>

E100#^#*#^#*#^#*#^#*#^#100

pepto-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)2>

E100#^#*#^#*#^#*#^#*#^#*#^#100

exto-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)(1)2>

E100#^##7

epto-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)(1)(1)2>

E100#^##8

ogdo-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)(1)(1)(1)2>

E100#^##9

ento-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)(1)(1)(1)(1)2>

{10,10(2)2}

xappol

One of Bowers original 120 googolisms. This is a 10x10 & 10s. It is believed to be slightly smaller than a dekato-godgahlah, which is believed to be larger since it is predicted to have 100 entry rows instead of 10 entry rows. It would be a 10x100 & 10s approximately.

E100#^##10

dekato-godgahlah

Approximately equal to <10,100(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)2>

E100#^##20

isosto-godgahlah

E100#^##100

gridgahlah / hecato-godgahlah

Approximately equal to <10,100(2)2>. This approximation is a 100 x 100 & 10s. This makes it larger than a xappol.

{10,xappol(2)2}

xappolplex

A xappol x xappol & 10s. This would be approximately equal to E100#^##xappol, making it larger than a gridgahlah but much much smaller than a gridtrigahlah.

E100#^##100#^##100

gridtrigahlah

Approximately equal to <10,100(2)3>

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

gridtergahlah

Approximately equal to <10,100(2)4>

E100#^##*#5

gridpeggahlah

Approximately equal to <10,100(2)5>

E100#^##*#6

gridhexgahlah

Approximately equal to <10,100(2)6>

E100#^##*#7

gridhepgahlah

Approximately equal to <10,100(2)7>

E100#^##*#8

grid-ahtgahlah

Approximately equal to <10,100(2)8>

E100#^##*#9

grid-enngahlah

Approximately equal to <10,100(2)9>

E100#^##*#10

grid-dekgahlah

Approximately equal to <10,100(2)10>

E100#^##*#^##100

deutero-gridgahlah

Approximately equal to <10,100(2)(2)2>. Approximately equal to 2 planes of 100x100 10s in array notation.

{3,3(3)2}

dimentri

This expands to {3,3(2)(2)(2)2} which becomes 3 planes. This is much much larger than the two planes of deutero-gridgahlah but it's much smaller than the 3 planes of a trito-gridgahlah.

E100#^##*#^##*#^##100

trito-gridgahlah

Approximately equal to <10,100(2)(2)(2)2>

E100#^##*#^##*#^##*#^##100

teterto-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)2>

E100#^###5

pepto-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)2>

E100#^###6

exto-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)(2)2>

E100#^###7

epto-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)(2)(2)2>

E100#^###8

ogdo-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)(2)(2)(2)2>

E100#^###9

ento-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)(2)(2)(2)(2)2>

{10,10(3)2} = 10^3 & 10s

colossal

A colossal is a 3-dimensional array of 10s of edge length 10. It has 10^3 or 1000 entries. That's a lot, though that is manageable and could be theoretically written out in full ... though it would be pretty tedious. This is just slightly smaller than dekato-gridgahlah which has 10 planes, but they are of size 100x100 instead of 10x10.

E100#^###10

dekato-gridgahlah

Approximately equal to <10,100(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)2>

E100#^###20

isosto-gridgahlah

Approximately equal to <10,100(2)...(2)2> w/20 (2)s

E100#^###100

kubikahlah / hecato-gridgahlah

Approximately equal to <10,100(3)2>. This would be a 100 x 100 x 100 & 10s. This would be much much larger than a dimentri, since a dimentri only has 3 planes, whereas this has 100.

{10,colossal(3)2} = colossal^3 & 10s

colossalplex

A 3-dimensional cube of edge length colossal all of 10s. This would fall below E100#^###100#2, which would be approximately a 3-dimensional cube of edge length kubikahlah all of 10s.

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

kubitrigahlah

Approximately equal to <10,100(3)3>

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

kubitergahlah

E100#^###*#5

kubipeggahlah

E100#^###*#6

kubihexgahlah

E100#^###*#7

kubihepgahlah

E100#^###*#8

kubi-ahtgahlah

E100#^###*#9

kubi-enngahlah

E100#^###*#10

kubi-dekahlah

E100#^###*#^###100

deutero-kubikahlah

E100#^###*#^###*#^###100

trito-kubikahlah

E100#^###*#^###*#^###*#^###100

teterto-kubikahlah

E100#^####5

pepto-kubikahlah

E100#^####6

exto-kubikahlah

E100#^####7

epto-kubikahlah

E100#^####8

ogdo-kubikahlah

E100#^####9

ento-kubikahlah

E100#^####10

dekato-kubikahlah

E100#^####20

isosto-kubikahlah

E100#^####100

quarticahlah / hecato-kubikahlah

Approximately equal to <10,100(4)2>

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

quartitrigahlah

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

quartitergahlah

E100#^####*#5

quartipeggahlah

E100#^####*#6

quartihexgahlah

E100#^####*#7

quartihepgahlah

E100#^####*#8

quarti-ahtgahlah

E100#^####*#9

quarti-enngahlah

E100#^####*#10

quarti-dekahlah

E100#^####*#^####100

deutero-quarticahlah

E100#^####*#^####*#^####100

trito-quarticahlah

E100#^####*#^####*#^####*#^####100

teterto-quarticahlah

E100#^#####5

pepto-quarticahlah

E100#^#####6

exto-quarticahlah

E100#^#####7

epto-quarticahlah

E100#^#####8

ogdo-quarticahlah

E100#^#####9

ento-quarticahlah

E100#^#####10

dekato-quarticahlah

E100#^#####20

isosto-quarticahlah

E100#^#####100

quinticahlah / hecato-quarticahlah

Approximately equal to <10,100(5)2>

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

quintitrigahlah

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

quintitergahlah

E100#^#####*#5

quintipeggahlah

E100#^#####*#6

quintihexgahlah

E100#^#####*#7

quintihepgahlah

E100#^#####*#8

quinti-ahtgahlah

E100#^#####*#9

quinti-enngahlah

E100#^#####*#10

quinti-dekahlah

E100#^#####*#^#####100

deutero-quinticahlah

E100#^#####*#^#####*#^#####100

trito-quinticahlah

E100#^#####*#^#####*#^#####*#^#####100

teterto-quinticahlah

E100#^######5

pepto-quinticahlah

E100#^######6

exto-quinticahlah

E100#^######7

epto-quinticahlah

E100#^######8

ogdo-quinticahlah

E100#^######9

ento-quinticahlah

E100#^######10

dekato-quinticahlah

E100#^######100

sexticahlah / hecato-quinticahlah

Approximately equal to <10,100(6)2>

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

sextitrigahlah

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

sextitergahlah

E100#^######*#5

sextipeggahlah

E100#^######*#6

sextihexgahlah

E100#^######*#7

sextihepgahlah

E100#^######*#8

sexti-ahtgahlah

E100#^######*#9

sexti-enngahlah

E100#^######*#10

sexti-dekahlah

E100#^######*#^######100

deutero-sexticahlah

E100#^######*#^######*#^######100

trito-sexticahlah

E100#^######*#^######*#^######*#^######100

teterto-sexticahlah

E100#^#######5

pepto-sexticahlah

E100#^#######6

exto-sexticahlah

E100#^#######7

epto-sexticahlah

E100#^#######8

ogdo-sexticahlah

E100#^#######9

ento-sexticahlah

E100#^#######10

dekato-sexticahlah

E100#^#######100

septicahlah / hecato-sexticahlah

Approximately equal to <10,100(7)2>

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

septitrigahlah

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

septitergahlah

E100#^#######*#5

septipeggahlah

E100#^#######*#6

septihexgahlah

E100#^#######*#7

septihepgahlah

E100#^#######*#8

septi-ahtgahlah

E100#^#######*#9

septi-enngahlah

E100#^#######*#10

septi-dekahlah

E100#^#######*#^#######100

deutero-septicahlah

E100#^#######*#^#######*#^#######100

trito-septicahlah

E100#^#######*#^#######*#^#######*#^#######100

teterto-septicahlah

E100#^########5

pepto-septicahlah

E100#^########6

exto-septicahlah

E100#^########7

epto-septicahlah

E100#^########8

ogdo-septicahlah

E100#^########9

ento-septicahlah

E100#^########10

dekato-septicahlah

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

octicahlah / hecato-septicahlah

Approximately equal to <10,100(8)2>

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

octitrigahlah

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

octitergahlah

E100#^########*#5

octipeggahlah

E100#^########*#6

octihexgahlah

E100#^########*#7

octihepgahlah

E100#^########*#8

octi-ahtgahlah

E100#^########*#9

octi-enngahlah

E100#^########*#10

octi-dekgahlah

E100#^########*#^########100

deutero-octicahlah

E100#^########*#^########*#^########100

trito-octicahlah

E100#^########*#^########*#^########*#^########100

teterto-octicahlah

E100#^#########5

pepto-octicahlah

E100#^#########6

exto-octicahlah

E100#^#########7

epto-octicahlah

E100#^#########8

ogdo-octicahlah

E100#^#########9

ento-octicahlah

E100#^#########10

dekato-octicahlah

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

nonicahlah

Approximately equal to <10,100(9)2>

{10,10(10)2} = 10^10 & 10s

dimendecal

This forms a 10-dimensional cube of edge length 10 all of 10s. It's a little smaller than a decicahlah, since a decicahlah is more like a 10-dimensional cube of edge length 100 all of 10s. A dimendecal has 10,000,000,000 entries!

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

decicahlah

Approximately equal to <10,100(10)2>

E100#^#^#11

undecicahlah

Approximately equal to <10,100(11)2>

E100#^#^#12

duodecicahlah

Approximately equal to <10,100(12)2>

E100#^#^#13

tredecicahlah

Approximately equal to <10,100(13)2>

E100#^#^#14

quattuordecicahlah

Approximately equal to <10,100(14)2>

E100#^#^#15

quindecicahlah

Approximately equal to <10,100(15)2>

E100#^#^#16

sexdecicahlah

Approximately equal to <10,100(16)2>

E100#^#^#17

septendecicahlah

Approximately equal to <10,100(17)2>

E100#^#^#18

octodecicahlah

Approximately equal to <10,100(18)2>

E100#^#^#19

novemdecicahlah

Approximately equal to <10,100(19)2>

E100#^#^#20

viginticahlah

Approximately equal to <10,100(20)2>

E100#^#^#30

triginticahlah

Approximately equal to <10,100(30)2>

E100#^#^#40

quadraginticahlah

Approximately equal to <10,100(40)2>

E100#^#^#50

quinquaginticahlah

Approximately equal to <10,100(50)2>

E100#^#^#60

sexaginticahlah

Approximately equal to <10,100(60)2>

E100#^#^#70

septuaginticahlah

Approximately equal to <10,100(70)2>

E100#^#^#80

octoginticahlah

Approximately equal to <10,100(80)2>

E100#^#^#90

nonaginticahlah

Approximately equal to <10,100(90)2>

{10,10(100)2}

gongulus

One of Bowers' most famous googolisms ... the gongulus. In a way, this combines Jonathan Bowers fascination with large numbers with his fascination of higher dimensions. This is a 100-dimensional cube of entries, of edge length 10 all of 10s. There would literally be a googol (10^100) entries in this expression. This means we would not be able to write it out in full. This number is only slightly smaller than a godgather, which brings us to ...

E100#^#^#100

godgathor

            A godgathor is comparable to Jonathan Bowers' gongulus. It's comparable to a 100-dimensional array. Evaluating godgathor we obtain:

E100#^#^#100 = E100#^#####...#####100 w/100 #s in a row

A godgathor should be greater than <10,100(100)2> which is larger than <10,10(100)2>. Thus a godgathor should be slightly larger than a gongulus. <10,100(100)2> is also equivalent to <10,100(0,1)2>

E100#^#101100

goober bunch

{10,10(gongulus)2}

gongulusplex

Now here is a cool number. It's a gongulus-dimensional cube of edge length 10 all of 10s. It would have a 10^gongulus entries, a gongulus-plexed entries if you will :p

This passes up the godgathor of course, but it's smaller than ...

E100#^#^#100#2

grand godgathor

E100#^#(1+E100#^#^(101)100)(E100#^#101100)

gibbering goober bunch

E100#^#^#100#3

grand grand godgathor

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

gotrigathor

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

gotergathor

E100#^#^#*#5

gopeggathor

E100#^#^#*#6

gohexgathor

E100#^#^#*#7

gohepgathor

E100#^#^#*#8

go-ahtgathor

E100#^#^#*#9

go-enngathor

E100#^#^#*#10

godekgathor

E100#^#^#*#^#^#100

deutero-godgathor

E100#^#^#*#^#^#*#^#^#100

trito-godgathor

E100#^#^#*#^#^#*#^#^#*#^#^#100

teterto-godgathor

E100#^(#^#*#)5

pepto-godgathor

E100#^(#^#*#)6

exto-godgathor

E100#^(#^#*#)7

epto-godgathor

E100#^(#^#*#)8

ogdo-godgathor

E100#^(#^#*#)9

ento-godgathor

E100#^(#^#*#)10

dekato-godgathor

E100#^(#^#*#)20

isosto-godgathor

E100#^(#^#*#)100

hecato-godgathor

Approximately equal to <10,100(1,1)2>

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

godgridgathor

Approximately equal to <10,100(2,1)2>. A 2-D array of 100-D arrays. More precisely it's a 100^2 array of 100^100 arrays.

{3,3(0,2)2}

dulatri

One of the original 120 named numbers by Jonathan Bowers. The notation {3,3(0,2)2} is modern and didn't exist back in 2002 when Bowers' first introduced this number. Originally it Bowers' defined it as a "(3^3)^2 array of 3's". Imagine a 3^3 array of 3^3 arrays. This can be seen by expanding the expression to the following:

{ 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (2,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (2,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 (1,1) 3^3&3 (0,1) 3^3&3 (0,1) 3^3&3 }

The "separators" here, are not themselves denoting additional "dimensions", at least not in the usual sense. Instead (0,1) separates any dimensional spaces. So the number of dimensions between (0,1) are not limited to 3, but any finite dimensional space. With that in mind, we can have "rows of dimensions" and "planes of dimensions" and so on. This can be thought of as going beyond infinite dimensional space, and continuing to (w+1)-dimensional space, (w+2)-dimensional space, and so on.

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

godkubikgathor

Approximately equal to <10,100(3,1)2>. A 3-D array of 100-D arrays. More precisely it's a 100^3 array of 100^100 arrays.

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

godquarticgathor

Approximately equal to <10,100(4,1)2>. A 4-D array of 100-D arrays.

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

godquinticgathor

Approximately equal to <10,100(5,1)2>. A 5-D array of 100-D arrays.

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

godsexticgathor

Approximately equal to <10,100(6,1)2>. A 6-D array of 100-D arrays.

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

godsepticgathor

Approximately equal to <10,100(7,1)2>. A 7-D array of 100-D arrays.

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

godocticgathor

Approximately equal to <10,100(8,1)2>. A 8-D array of 100-D arrays.

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

godnonicgathor

Approximately equal to <10,100(9,1)2>. A 9-D array of 100-D arrays.

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

goddecicgathor

Approximately equal to <10,100(10,1)2>. A 10-D array of 100-D arrays.

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

godgathordeus

Approximately equal to <10,100(0,2)2> = <10,100(100,1)2>. This would be much larger than a dulatri even though this is also a dimension array of dimension arrays. However in this case it's a 100-dimensional array of 100-dimensional arrays.

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

hecato-godgathordeus

Approximately equal to <10,100(1,2)2>

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

godgridgathordeus

Approximately equal to <10,100(2,2)2>

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

godkubikgathordeus

Approximately equal to <10,100(3,2)2>

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

godquarticgathordeus

Approximately equal to <10,100(4,2)2>

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

godquinticgathordeus

Approximately equal to <10,100(5,2)2>

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

godsexticgathordeus

Approximately equal to <10,100(6,2)2>

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

godsepticgathordeus

Approximately equal to <10,100(7,2)2>

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

godocticgathordeus

Approximately equal to <10,100(8,2)2>

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

godnonicgathordeus

Approximately equal to <10,100(9,2)2>

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

goddecicgathordeus

Approximately equal to <10,100(10,2)2>

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

godgathortruce

Approximately equal to <10,100(100,2)2> = <10,100(0,3)2>

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

godgathorquad

Approximately equal to <10,100(0,4)2>

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

godgathorquid

Approximately equal to <10,100(0,5)2>

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

godgathorsid

Approximately equal to <10,100(0,6)2>

E100#^#^##7

godgathorseptuce

Approximately equal to <10,100(0,7)2>

E100#^#^##8

godgathoroctuce

Approximately equal to <10,100(0,8)2>

E100#^#^##100

gralgathor

Approximately equal to <10,100(0,0,1)2>

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

graltrigathor

Approximately equal to <10,100(0,0,1)3>

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

graltergathor

Approximately equal to <10,100(0,0,1)4>

E100#^#^##*#^#^##100

deutero-gralgathor

Approximately equal to <10,100(0,0,1)(0,0,1)2>

E100#^#^##*#^#^##*#^#^##100

trito-gralgathor

Approximately equal to <10,100(0,0,1)(0,0,1)(0,0,1)2>

E100#^#^##*#^#^##*#^#^##*#^#^##100

teterto-gralgathor

Approximately equal to <10,100(0,0,1)(0,0,1)(0,0,1)(0,0,1)2>

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

gralgathordeus

Approximately equal to <10,100(0,0,2)2>

{3,3(0,0,0,1)2}

trimentri

One of Bowers' original 120 named numbers. This array is also equivalent to {3,3(0,0,3)2}, which is clearly smaller than a gralgathortruce but larger than gralgathordeus.

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

gralgathortruce

Approximately equal to <10,100(0,0,3)2>

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

gralgathorquad

Approximately equal to <10,100(0,0,4)2>

E100#^#^###5

gralgathorquid

Approximately equal to <10,100(0,0,5)2>

E100#^#^###6

gralgathorsid

Approximately equal to <10,100(0,0,6)2>

E100#^#^###7

gralgathorseptuce

Approximately equal to <10,100(0,0,7)2>

E100#^#^###8

gralgathoroctuce

Approximately equal to <10,100(0,0,8)2>

E100#^#^###100

thraelgathor

Approximately equal to <10,100(0,0,0,1)2>

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

thraeltrigathor

Approximately equal to <10,100(0,0,0,1)3>

E100#^#^###*#^#^###100

deutero-thraelgathor

Approximately equal to <10,100(0,0,0,1)(0,0,0,1)2>

E100#^#^###*#^#^###*#^#^###100

trito-thraelgathor

Approximately equal to <10,100(0,0,0,1)(0,0,0,1)(0,0,0,1)2>

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

thraelgathordeus

Approximately equal to <10,100(0,0,0,2)2>

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

thraelgathortruce

Approximately equal to <10,100(0,0,0,3)2>

E100#^#^####100

terinngathor

Approximately equal to <10,100(0,0,0,100)2> = <10,100(0,0,0,0,1)2>

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

terinntrigathor

Approximately equal to <10,100(0,0,0,0,1)3>

E100#^#^####*#^#^####100

deutero-terinngathor

Approximately equal to <10,100(0,0,0,0,1)(0,0,0,0,1)2>

E100#^#^####*#^#^####*#^#^####100

trito-terinngathor

Approximately equal to <10,100(0,0,0,0,1)(0,0,0,0,1)(0,0,0,0,1)2>

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

terinngathordeus

Approximately equal to <10,100(0,0,0,0,2)2>

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

terinngathortruce

Approximately equal to <10,100(0,0,0,0,3)2>

E100#^#^#####100

pehaelgathor

Approximately equal to <10,100(0,0,0,0,100)2> = <10,100(0,0,0,0,0,1)2> 

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

hexaelgathor

Approximately equal to <10,100(0,0,0,0,0,100)2> = <10,100(0,0,0,0,0,0,1)2>

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

heptaelgathor

Approximately equal to <10,100(0,0,0,0,0,0,100)2> = <10,100(0,0,0,0,0,0,0,1)2>

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

octaelgathor

Approximately equal to <10,100(0,0,0,0,0,0,0,100)2> = <10,100(0,0,0,0,0,0,0,0,1)2>

E100#^#^#^#100

godtothol

Approximately equal to <10,100(0,0,...,0,0,1)2> w/100 0s. This can also be simplified to <10,100(0(1)1)2>. At this point we have reached X^X^X arrays.

E100#^#^#^##100

graltothol

E100#^#^#^###100

thraeltothol

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

terinntothol

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

pehaeltothol

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

hexaeltothol

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

heptaeltothol

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

octaeltothol

E100#^#^#^#^#100

godtertathol

Approximately equivalent to X^X^X^X arrays.

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

graltertathol

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

thraeltertathol

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

terinntertathol

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

pehaeltertathol

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

hexaeltertathol

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

heptaeltertathol

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

octaeltertathol

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

godpeptathol

Approximately equivalent to X^^5 arrays.

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

gralpeptathol

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

thraelpeptathol

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

terinnpeptathol

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

pehaelpeptathol

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

hexaelpeptathol

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

heptaelpeptathol

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

octaelpeptathol

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

godextathol

Approximately equivalent to X^^6 arrays.

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

gralextathol

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

thraelextathol

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

terinnextathol

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

pehaelextathol

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

hexaelextathol

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

heptaelextathol

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

octaelextathol

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

godeptathol

Approximately equivalent to X^^7 arrays.

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

graleptathol

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

thraeleptathol

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

terinneptathol

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

pehaeleptathol

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

hexaeleptathol

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

heptaeleptathol

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

octaeleptathol

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

godoctathol

Approximately equivalent to X^^8 arrays.

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

graloctathol

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

thraeloctathol

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

terinnoctathol

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

pehaeloctathol

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

hexaeloctathol

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

heptaeloctathol

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

octaeloctathol

E100#^^#100

tethrathoth

            The tethrathoth (or simply thoth) is equal to E100#^#^#^#^ ... ^#^#^#^#100 w/100 #s. It is comparable and slightly smaller than Jonathan Bowers' goppatoth. It is roughly equivalent to an X^^99 array.

10^^100 & 10

goppatoth

One of Bowers' largest of his original set of 121 googolisms. This one is interesting in being at the limit of what is considered to be well defined in array notation (even to this day!). This would be a tetrational array. Specifically it would be a X^^100 array, making it just slightly larger than a tethrathoth. In fact, a goppatoth should be approximately E100#^^#101 in ExE.

E100,000#^^#100,000

tethrathothigong

            For old time sake, here is the "gong" version of a tethrathoth, the tethrathothigong. It is equal to E100,000#^#^#^#^...^#^#^#^#100,000 w/100,000 #s. Technically speaking this number is mind-crushingly larger than having a mere hundred cascade levels ... but it's still a very modest improvement compare to how far we're going to take it from here ...

E100#^^#100#2

grand tethrathoth

            The grand tethrathoth is equal to E100#^#^#^#^ ... ^#^#^#^#100 w/tethrathoth #s. This is incomparably larger than the tethrathothigong, though from a googologist's perspective just a stone's skip away from the tethrathoth. It is comparable to and slightly smaller than Jonathan Bowers' goppatothplex. It is roughly equivalent to a X^^(tethrathoth-1) array. The next explicitly named googolism after a goppatothplex is a triakulus. This number is much much MUCH larger and it will take us a long time to reach it!

10^^goppatoth & 10

goppatothplex

A X^^goppatoth array. This makes it just "slightly" larger than a grand tethrathoth. This is notable for being the last well-defined googolism of Bowers' original set. The next Bowerism of the original set is a tridecatrix, which is {10,10,10} & 10. However pentational arrays have never been formally defined, let along dekational arrays! These will be added for size reference regardless, based on there theoretical placement. 

E100,000#^^#100,000#2

grand tethrathothigong

E100#^^#100#3

grand grand tethrathoth

E100#^^#100#4

grand grand grand tethrathoth

E100#^^#100#5

grand grand grand grand tethrathoth

E100#^^#100#6

grand grand grand grand grand tethrathoth

E100#^^#100#7

grand grand grand grand grand grand tethrathoth

E100#^^#100#100

ninety-nine-ex-grand tethrathoth / grantethrathoth

E100#^^#100#101

hundred-ex-grand tethrathoth

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

googol-ex-grand tethrathoth

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

googolplex-ex-grand tethrathoth

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

grangol-ex-grand tethrathoth

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

gugold-ex-grand tethrathoth

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

godgahlah-ex-grand tethrathoth

E100#^^#100#1#2

tethrathoth-minus-one-ex-grand tethrathoth

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

tethrathoth-ex-grand tethrathoth

E100#^^#100#2#2

grand-tethrathoth-minus-one-ex-grand tethrathoth

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

grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#3#2

grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

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

grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#4#2

grand-grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

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

grand-grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#5#2

grand-grand-grand-grand-tethrathoth-minus-one-ex-grand tethrathoth

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

grand-grand-grand-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#3

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

tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#2#3

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

grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#3#3

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

grand-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#4

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

tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#5

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

tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand-tethrathoth-ex-grand tethrathoth

E100#^^#100#1#100

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

w/100 E100#^^#100s

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

            A modest attempt to extend the tethrathoth using the obvious approach of extending the sequence: tethrathoth, grand tethrathoth, grand grand tethrathoth, three-ex-grand tethrathoth, four-ex-grand tethrathoth, ... etc. This extension however is not as ambitious as it seems! This number is still smaller than a greatethrathoth.

E100#^^#100#100#100

greatethrathoth

E100#^^#100#1#1#2

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

w/tethrathoth E100#^^#100s

tethrathoth-ex-grand-tethrathoth-ex-grand- ... ... -tethrathoth-ex-grand tethrathoth

w/tethrathoth "tethrathoth"s

            How crazy is that?! This is the sort of number someone might come up with the extend the tethrathoth series given the notation N-ex-grand tethrathoth is the (N+1)th member of the tethrathoth series. Yet it barely taps into the possibilities with Extended Cascading-E Notation (xE^). It's still smaller than a grand greatethrathoth.

E100#^^#100#100#100#2

grand greatethrathoth

E100#^^#100#1#1#3

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

w/E100#^^#100#(1+E100#^^#100#(...(1+E100#^^#100))...)) "E100#^^#100"s 

w/tethrathoth "E100#^^#100"s

tethrathoth-ex-grand-tethrathoth-ex-grand- ... ... -tethrathoth-ex-grand tethrathoth

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

w/tethrathoth "tethrathoth"s

            This is just insane!!! Yet this is clearly the wrong approach because even torturing language this far doesn't get us as far as a mere grand grand greatethrathoth. This again shows the linguistic approach is vastly inferior to the mathematical approach.

E100#^^#100#100#100#3

grand grand greatethrathoth

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

gigantethrathoth

E100#^^#100#1#1#1#2

tethrathoth-ex- ... ... -ex-grand-tethrathoth-ex-grand tethrathoth

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

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

...

...

...

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

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

w/tethrathoth "tethrathoth"s

where there are a tethrathoth lines

            Despite how insane this is, it's still doesn't get one very far. This is still less than a grand gigantethrathoth.

E100#^^#100#100#100#100#2

grand gigantethrathoth

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

gorgetethrathoth

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

gultethrathoth

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

gasptethrathoth

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

ginortethrathoth

E100#^^#100##100

E100#^^#100###100

E100#^^#100####100

E100#^^#100#^#100

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

E100#^^#100#^#*#100

E100#^^#100#^#*##100

E100#^^#100#^#*###100

E100#^^#100#^#*#^#100

E100#^^#100#^#*#^#*#^#100

E100#^^#100#^##100

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

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

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

E100#^^#100#^^#100 

tethratrithoth

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

tethraterthoth

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

tethrapethoth

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

tethra-exthoth

E100#^^#*#7

tethra-epthoth

E100#^^#*#8

tethra-octhoth

E100#^^#*#100

E100#^^#*##100

E100#^^#*###100

E100#^^#*#^#100

E100#^^#*#^##100

E100#^^#*#^###100

E100#^^#*#^####100

E100#^^#*#^#^#100

E100#^^#*#^#^#^#100

E100#^^#*#^^#100

 deutero-tethrathoth

E100#^^#*#^^#*#^^#100 

trito-tethrathoth

E100#^^#*#^^#*#^^#*#^^#100

teterto-tethrathoth

E100(#^^#)^#100

hecato-tethrathoth

E100(#^^#)^#100#2

grand hecato-tethrathoth

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

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

E100(#^^#)^##100

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Monster-Giant

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

Super Monster-Giant

E100(#^^#)^^#100

terrible tethrathoth

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

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

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

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

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

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

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

deutero-terrible tethrathoth

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

trito-terrible tethrathoth

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

hecato-terrible tethrathoth

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

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

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

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

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

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

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

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

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

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

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

terrible terrible tethrathoth

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

terrible terrible terrible tethrathoth

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

terrible terrible terrible terrible tethrathoth

E100#^^#>#100

tethriterator

or

 tethrathoth ba'al

or

ninety-nine-ex-terrible tethrathoth

This number begins to push the limits of LECEN. In xE^ however this can be compactly expressed as E100#^^#>#100, using the new #^^#># delimiter which diagonalizes over LECEN with the fundamental sequence:

#^^#>#[1] = #^^#

#^^#>#[n] = (#^^#>#[n-1])^^#

With this in place it now becomes trivial to move way way beyond LECEN...

E100#^^#>#(1+E100)

googol-ex-terrible tethrathoth

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

grangol-ex-terrible tethrathoth

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

greagol-ex-terrible tethrathoth

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

gigangol-ex-terrible tethrathoth

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

gorgegol-ex-terrible tethrathoth

gulgol-ex-terrible tethrathoth

gaspgol-ex-terrible tethrathoth

ginorgol-ex-terrible tethrathoth

gugold-ex-terrible tethrathoth

gugolthra-ex-terrible tethrathoth

throogol-ex-terrible tethrathoth

teroogol-ex-terrible tethrathoth

godgahlah-ex-terrible tethrathoth

gridgahlah-ex-terrible tethrathoth

kubikahlah-ex-terrible tethrathoth

quarticahlah-ex-terrible tethrathoth

quinticahlah-ex-terrible tethrathoth

sexticahlah-ex-terrible tethrathoth

septicahlah-ex-terrible tethrathoth

octicahlah-ex-terrible tethrathoth

nonicahlah-ex-terrible tethrathoth

decicahlah-ex-terrible tethrathoth

viginticahlah-ex-terrible tethrathoth

nonaginticahlah-ex-terrible tethrathoth

godgathor-ex-terrible tethrathoth

goober bunch-ex-terrible tethrathoth

gralgathor-ex-terrible tethrathoth

thraelgathor-ex-terrible tethrathoth

terinngathor-ex-terrible tethrathoth

godtothol-ex-terrible tethrathoth

graltothol-ex-terrible tethrathoth

thraeltothol-ex-terrible tethrathoth

terinntothol-ex-terrible tethrathoth

godtertathol-ex-terrible tethrathoth

graltertathol-ex-terrible tethrathoth

godpeptathol-ex-terrible tethrathoth

godextathol-ex-terrible tethrathoth

godeptathol-ex-terrible tethrathoth

godoctathol-ex-terrible tethrathoth

tethrathoth-ex-terrible tethrathoth

grand tethrathoth-ex-terrible tethrathoth

Monster-Giant-ex-terrible tethrathoth

Super Monster-Giant-ex-terrible tethrathoth

terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

terrible-terrible-terrible-terrible-tethrathoth-ex-terrible tethrathoth

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

w/tethrathoth ba'al "^^#"s

Great and Terrible Tethrathoth

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

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 is as far as I've developed Extended Cascading-E Notation (xE^) at the moment. It's still a VERY VERY VERY VERY ... VERY VERY LONG WAY to pentational arrays. In the next catagory are some unimaginably vast numbers which currently no one quite knows where they should fall on the Fast-growing hierarchy...