Triggolbong = {10,10,10,10^8,2}
Triggolthrong = {10,10,10,10^11,2}
Traggolgong = {10,10,10,10^5,3}
Traggolbong = {10,10,10,10^8,3}
Traggolthrong = {10,10,10,10^11,3}
Treegolthrong = {10,10,10,10^11,4}
Trigolgong = {10,10,10,10^5,5}
Trigolbong = {10,10,10,10^8,5}
Trigolthrong = {10,10,10,10^11,5}
We can continue
Troggolgong = {10,10,10,10^5,6}
Tragolgong = {10,10,10^5,7}
... ... ...
Pentadecal = {10,10,10,10,10}
Quadroogol = {10,10,10,10,100}
Quadroogolgong = {10,10,10,10,100000}
Quadroogolbong = {10,10,10,10,10^8}
Quadroogolthrong = {10,10,10,10,10^11}
Quadroogolplex = {10,10,10,10,{10,10,10,10,100}}
...
Quadroogoogol = {10,100,1,1,1,2}
Quadroogiggol = {10,100,2,1,1,2}
Quadroogaggol = {10,100,3,1,1,2}
...
Quadrooboogol = {10,10,100,1,1,2}
Quadrootroogol = {10,10,10,100,1,2}
Quadriggol = {10,10,10,10,100,2}
Quadriggoogol = {10,100,1,1,1,3}
Quadriggiggol = {10,100,2,1,1,3}
...
Now you can see where this is going. Let's skip a few ...
Septiggol = {10,10,10,10,10,10,10,100,2}
Septaggol = {10,10,10,10,10,10,10,100,3}
Septeegol = {10,10,10,10,10,10,10,100,4}
Septigol = {10,10,10,10,10,10,10,100,5}
Septoggol = {10,10,10,10,10,10,10,100,6}
Septagol = {10,10,10,10,10,10,10,100,7}
Octadecal = {10,8(1)2}
Nonadecal/Ennadecal = {10,9(1)2}
Iteral = {10,10(1)2}
Goobol = {10,100(1)2}
Gibbol = {10,100,2(1)2}
Gabbol = {10,100,3(1)2}
...
Gootrol = {10,100(1)3}
...
Gossol = {10,10(1)100}
Gossogoogol = {10,100(1)1,2}
Gossogiggol = {10,100,2(1)1,2}
...
Gossbol = {10,100(1)2,2}
Gosstrol = {10,100(1)3,2}
Gossquadrol = {10,100(1)4,2}
Gossquintol = {10,100(1)5,2}
...
Gissol = {10,10(1)100,2}
Gassol = {10,10(1)100,3}
...
Mossol = {10,10(1)10,100}
Mossogoogol = {10,100(1)1,1,2}
Mossogiggol = {10,100,2(1)1,1,2}
...
Mossbabol = {10,100(1)1,2,2}
Mossba-babol = {10,100(1)2,2,2}
...
Mossbatrol = {10,100(1)1,3,2}
...
Missol = {10,10(1)10,100,2}
...
Bossol = {10,10(1)10,10,100}
Bossogoogol = {10,100(1)1,1,1,2}
... ... ...
Dubol = {10,100(1)(1)2}
Dubogiggol = {10,100,2(1)(1)2}
...
Dubogoobol = {10,100(1)2 (1)(1)2} [I'm not sure how to write that correctly]
...
Dubtrol = {10,100(1)(1)3}
Dubquadrol = {10,100(1)(1)4}
...
...
Triubol = {10,100(1)(1)(1)2}
... ... ...
Goxxogiggol = {10,100,2(2)2}
... ... ...
Coloxxogiggol = {10,100,2(3)2}
As you can see I'm replacing the "l" at the end of all of these names with the name of the number we want to "-carta-" or add ordinals.
To understand what I mean by "carta" and "by", here's an example:
let & be any delimiter.
let % be a delimiter "bigger" than &. eg {#,#,1,2} >> #^^# > #^#^# > #^## > #^#*#^# > #^#*# > #^# > ### > ## > #
so, &-carta-% is defined as: E n % n & n, where n is the "root", usually 100.
the carta operator "adds" ordinals. so if ord([delimiter]) returns the ordinal of a hyperion-stack, then ord(&-carta-%) = ord(%) + ord(&)
%-by-& is similarly just "multiplying" hyperions, stated as %*& in ExE.
How would I "multiply" hyperions for the larger numbers above gongulus? We can simply use 'mul' (shortening of 'multiply')
gongulus = {10,10(100)2}
gongulgiggol = {10,100,2(0,1)2}
gongulus-mul-two = {10,100(0,1)3}
...
gongulus-mul-root = {10,10(0,1)100}
...this allows us to go all the way to...
gongulus-mul-gongulus-mul-gongulus-mul-gongulus-mul-gongulus-mul-...
We need a shortening. but now we have reached exponentiation! we can just use -pow-.
but after that we have NOT reached tetration yet! remember here we are using LEFT-ASSOCIATIVE powers, and that means the growth rate we have achieved is only somewhere around n^n^n-1.
To solve this dilemma we need to have a look at how Sbiis solved this problem.
gongulus ~ E10#^#^#100
gongulus-pow-root ~ E10#^(#^#*#)100 = E10(#^#^#)^#100 ~ fgh w^w^(w+1)
(same as gongulusblast = {10,100(1,1)2})
gongulus-pow-boogol = {10,100(1,1)(1,1)2}
gongulus-pow-goobol = {10,100(2,1)2} ~ E10#^(#^#*##)100
(same as gonzapgulus = {10,100(2,1)2})
...
gongulus-pow-gongulus = {10,100(0,2)2}~ E10#^(#^#*#^#)100
(same as gingulus = {10,100(0,2)2})
...
then we reach gralgathor in exe, which means that we have reached...
bongulus = {10,100(0,0,1)2}
trongulus = {10,100(0,0,0,1)2}
...
goplexulus = {10,100((1)1)2}
goplexulgiggol = {10,100,2((1)1)2}
...
goplexulus-mul-root = {10,10((1)1)100}
...
goplexulus-pow-goplexulus ~ E10#^(#^#^#*#^#^#)100
goplexulus-pow-goplexulus-pow-goplexulus ~ E10#^(#^#^#*#^#^#*#^#^#)100
? ~ E10#^#^(#^#*#)100
What should we call this number? When we reached here previous time we "neglected" making a naming system for this because we had already reached gingulus.
we can maybe use hyper- like sbiis. simple is best.
(we haven't reached tetration yet!!)
hyper-gongulus-pow-root = hyper-hyper-goobol-mul-root ~ E10#^#^(#^#*#)100
hyper-gongulus-pow-gongulus = hyper-hyper-goobol-mul-goobol = {10,100((1)(1)1)2} ~ E10#^#^(#^#*#^#)100 = giplexulus
AND THEN WE REACH
boplexulus = {10,100((2)1)2} ~ E10#^#^#^##100
troplexulus = {10,100((3)1)2}
goduplexulus = {10,10((100)1)2} = {10,100((0,1)1)2} = {10,10[1[100]2]2} = {10,100[1[1,2]2]2}
with our hyper operator we can already formalize everything until...
goppatoth = 10^^100 & 10
now bowers' notation is SIMPLY TOO AWKWARD and UN-FORMALIZED.
(ill be using same notation as xrq here )
goppatoth = {10,100([1]1)2}
goppatoth-pow-root = {10,100(1[1]1)2} (comparable to tethrafact, same as "goppatothblast" / "goppatothfact")
...
TBC
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