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This page documents the many derivatives of Googol.
THIS LIST IS A WORK IN PROGRESS
Base
Most extensions of Googol were coined by Johnathan Bowers and are based around his notation Bowers' Exploding Array Function, or BEAF, which Bird's Array Notation (BAN) is based on. Each extension will be defined based on how it affects Googol written in BEAF.
Notations
Scientific/Knuth's Up-arrow/Operator/BEAF
(Notations will be dropped as they become impractical for writing the number)
Googol
10^100/10↑100/10{1}100/{10, 100}
Tier 1 - Suffixes
These replace the 100 with a larger power of 10 like so:
-chime - 1,000 -toll - 10,000 -gong - 100,000 -bong - 100,000,000 -throng - 100,000,000,000 -gandigan - 100,000,000,000,000
You could possibly keep going with -quintigong for 100 quadrillion, but these are the ones seen in MathisR.V's video.
Googolchime
10^1,000/10↑1,000/10{1}1,000/{10, 1,000}
Googoltoll
10^10,000/10↑10,000/10{1}10,000/{10, 10,000}
Googolgong
10^100,000/10↑100,000/10{1}100,000/{10, 100,000}
Googolbong
10^100,000,000/10↑100,000,000/10{1}100,000,000/{10, 100,000,000}
Googolthrong
10^100,000,000,000/10↑100,000,000,000/10{1}100,000,000,000/{10, 100,000,000,000}
Googolgandigan
10^100,000,000,000,000/10↑100,000,000,000,000/10{1}100,000,000,000,000/{10, 100,000,000,000,000}
Tier 2 - -plexes
These replace the 100 with nested Googols (or later variants). They use Greek/Latin prefixes in their names counting how much nesting there is. -triplex adds -duplex, -quadriplex adds -triplex, etc.
Googolplex
(the only officially recognized Googol extension)
10^10^100/10↑10↑100/10{1}10{1}100/{10, {10, 100}}
Googolplexichime
10^10^1,000/10↑10↑1,000/10{1}10{1}1,000/{10, {10, 1,000}}
Googolplexitoll
10^10^10,000/10↑10↑10,000/10{1}10{1}10,000/{10, {10, 10,000}}
Googolplexigong
10^10^100,000/10↑10↑100,000/10{1}10{1}100,000/{10, {10, 100,000}}
Googolplexibong
10^10^100,000,000/10↑10↑100,000,000/10{1}10{1}100,000,000/{10, {10, 100,000,000}}
Googolplexithrong
10^10^100,000,000,000/10↑10↑100,000,000,000/10{1}10{1}100,000,000,000/{10, {10, 100,000,000,000}}
Googolplexigandigan
10^10^100,000,000,000,000/10↑10↑100,000,000,000,000/10{1}10{1}100,000,000,000,000/{10, {10, 100,000,000,000,000}}
Googolduplex
(also recognized, kinda, as Googolplexian)
10^10^10^100/10↑10↑10↑100/10{1}10{1}10{1}100/{10, {10, {10, 100}}}
Googoltriplex
10^10^10^10^100/10↑10↑10↑10↑100/10{1}10{1}10{1}10{1}100/{10, {10, {10, {10, 100}}}}
Googolquadriplex
10^10^10^10^10^100/10↑10↑10↑10↑10↑100/10{1}10{1}10{1}10{1}10{1}100/{10, {10, {10, {10, {10, 100}}}}}
Googolquintiplex
10^10^10^10^10^10^100/10↑10↑10↑10↑10↑10↑100/10{1}10{1}10{1}10{1}10{1}10{1}100/{10, {10, {10, {10, {10, {10, 100}}}}}}
Googolsextiplex
10^10^10^10^10^10^10^100/(10↑)^7 100/(10{1})^7 100/{10, {10, {10, {10, {10, {10, {10, 100}}}}}}}
(At this point, the notations get so long that Up-Arrow and Operator Notation have to be compressed to fit on one line of text.)
Googolseptiplex
10^10^10^10^10^10^10^10^100/(10↑)^8 100/(10{1})^8 100/{10, {10, {10, {10, {10, {10, {10, {10, 100}}}}}}}}
Googoloctiplex
10^10^10^10^10^10^10^10^10^100/(10↑)^9 100/(10{1})^9 100/{10, {10, {10, {10, {10, {10, {10, {10, {10, 100}}}}}}}}}
Googolnoniplex
10^10^10^10^10^10^10^10^10^10^100/(10↑)^10 100/(10{1})^10 100/{10, {10, {10, {10, {10, {10, {10, {10, {10, {10, 100}}}}}}}}}}
Googoldeciplex
10^10^10^10^10^10^10^10^10^10^10^100/(10↑)^11 100/(10{1})^11 100/{10, {10, {10, {10, {10, {10, {10, {10, {10, {10, {10, 100}}}}}}}}}}}
Tier 3 - Replacing -oo-
These put an entry after the 100 like so:
-ig- - 2 -ag- - 3 -ee- - 4 -i- - 5 -og- - 6 -a- - 7
Giggol
10↑↑100/10{2}100/{10, 100, 2}
Giggolchime
10↑↑1,000/10{2}1,000/{10, 1,000, 2}
Giggoltoll
10↑↑10,000/10{2}10,000/{10, 10,000, 2}
Giggolgong
10↑↑100,000/10{2}100,000/{10, 100,000, 2}
Giggolbong
10↑↑100,000,000/10{2}100,000,000/{10, 100,000,000, 2}
Giggolthrong
10↑↑100,000,000,000/10{2}100,000,000,000/{10, 100,000,000,000, 2}
Giggolgandigan
10↑↑100,000,000,000,000/10{2}100,000,000,000,000/{10, 100,000,000,000,000, 2}
Giggolplex
10↑↑10↑↑100/10{2}10{2}100/{10, {10, 100, 2}, 2}
Giggolduplex
10↑↑10↑↑10↑↑100/10{2}10{2}10{2}100/{10, {10, {10, 100, 2}, 2}, 2}
Giggoltriplex
10↑↑10↑↑10↑↑10↑↑100/10{2}10{2}10{2}10{2}100/{10, {10, {10, {10, 100, 2}, 2}, 2}, 2}
Gaggol
10↑↑↑100/10{3}100/{10, 100, 3}
Geegol
10↑↑↑↑100/10{4}100/{10, 100, 4}
Gigol
10↑↑↑↑↑100/10{5}100/{10, 100, 5}
Goggol
10↑↑↑↑↑↑100/10{6}100/{10, 100, 6}
Gagol
10{7}100/{10, 100, 7}
Tier 4 - Replacing G-
These add more 10s before the 100. The first G in Googol is replaced with a Greek/Latin prefix based on the number of 10s.
Boogol
10{100}10/{10, 10, 100}
Boogolchime
10{1,000}10/{10, 10, 1,000}
Boogoltoll
10{10,000}10/{10, 10, 10,000}
Boogolgong
10{100,000}10/{10, 10, 100,000}
Boogolbong
10{100,000,000}10/{10, 10, 100,000,000}
Boogolthrong
10{100,000,000,000}10/{10, 10, 100,000,000,000}
Boogolgandigan
10{100,000,000,000,000}10/{10, 10, 100,000,000,000,000}
Boogolplex
10{10{100}10}10}/{10, 10, {10, 10, 100}}
Boogolduplex
10{10{10{100}10}10}10/{10, 10, {10, 10, {10, 10, 100}}}
Boogoltriplex
10{10{10{10{100}10}10}10}10/{10, 10, {10, 10, {10, 10, {10, 10, 100}}}}
Biggol
10{{100}}10/{10, 10, 100, 2}
Baggol
10{{{100}}}10/{10, 10, 100, 3}
Beegol
10{{{{10}}}}10/{10, 10, 100, 4}
Bigol
10{{{{{100}}}}}10/{10, 10, 100, 5}
Boggol
10{{{{{{100}}}}}}10/{10, 10, 100, 6}
Bagol
10{{{{{{{100}}}}}}}10/{10, 10, 100, 7}
Troogol
{10, 10, 10, 100}
Quadroogol
{10, 10, 10, 10, 100}
Quintoogol
{10, 10, 10, 10, 10, 100}
Sextoogol
{10, 10, 10, 10, 10, 10, 100}
Septoogol
{10, 10, 10, 10, 10, 10, 10, 100}
Octoogol
{10, 10, 10, 10, 10, 10, 10, 10, 100}
Nonoogol
{10, 10, 10, 10, 10, 10, 10, 10, 10, 100}
Decoogol
{10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 100}
Tier 5 - Replacing -g-
These add (1) followed by a single entry based on the extension. The extensions themselves are the same as tier 4, but applied to the second g.
(An array ending in (1) 1 is the same as an array without any (1) separators, eg. {10, 50, 4 (1) 1} = {10, 50, 4})
Goobol
{10, 100 (1) 2}/{10, 100 [2] 2}
Goobolchime
{10, 1,000 (1) 2}/{10, 1,000 [2] 2}
Gooboltoll
{10, 10,000 (1) 2}/{10, 10,000 [2] 2}
Goobolgong
{10, 100,000 (1) 2}/{10, 100,000 [2] 2}
Goobolbong
{10, 100,000,000 (1) 2}/{10, 100,000,000 [2] 2}
Goobolthrong
{10, 100,000,000,000 (1) 2}/{10, 100,000,000,000 [2] 2}
Goobolgandigan
{10, 100,000,000,000,000 (1) 2}/{10, 100,000,000,000,000 [2] 2}
Goobolplex
{10, {10, 100 (1) 2} (1) 2}/{10, {10, 100 [2] 2} [2] 2}
Goobolduplex
{10, {10, {10, 100 (1) 2} (1) 2} (1) 2}/{10, {10, {10, 100 [2] 2} [2] 2} [2] 2}
Gooboltriplex
{10, {10, {10, {10, 100 (1) 2} (1) 2} (1) 2} (1) 2}/{10, {10, {10, {10, 100 [2] 2} [2] 2} [2] 2} [2] 2}
Gibbol
{10, 100, 2 (1) 2}/{10, 100, 2 [2] 2}
Gabbol
{10, 100, 3 (1) 2}/{10, 100, 3 [2] 2}
Geebol
{10, 100, 4 (1) 2}/{10, 100, 4 [2] 2}
Gibol
{10, 100, 5 (1) 2}/{10, 100, 5 [2] 2}
Gobbol
{10, 100, 6 (1) 2}/{10, 100, 6 [2] 2}
Gabol
{10, 100, 7 (1) 2}/{10, 100, 7 [2] 2}
Boobol
{10, 10, 100 (1) 2}/{10, 10, 100 [2] 2}
Troobol
{10, 10, 10, 100 (1) 2}/{10, 10, 10, 100 [2] 2}
Quadroobol
{10, 10, 10, 10, 100 (1) 2}/{10, 10, 10, 10, 100 [2] 2}
Quintoobol
{10, 10, 10, 10, 10, 100 (1) 2}/{10, 10, 10, 10, 10, 100 [2] 2}
Gootrol
{10, 100 (1) 3}/{10, 100 [2] 3}
Gooquadrol
{10, 100 (1) 4}/{10, 100 [2] 4}
Gooquintol
{10, 100 (1) 5}/{10, 100 [2] 5}
Goosextol
{10, 100 (1) 6}/{10, 100 [2] 6}
Gooseptol
{10, 100 (1) 7}/{10, 100 [2] 7}
Goooctol
{10, 100 (1) 8}/{10, 100 [2] 8}
Goonongol
{10, 100 (1) 9}/{10, 100 [2] 9}
Goodecol
{10, 100 (1) 10}/{10, 100 [2] 10}
Tier 6 - Gossols
These alter the structure significantly, with the 100 now on the other side of the (1) separator.
Tier 3 is ignored, and tier 4 has an extra M- step added.
Gossol
{10, 10 (1) 100}/{10, 10 [2] 100}
Gossolchime
{10, 10 (1) 1,000}/{10, 10 [2] 1,000}
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