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Gaggol is equal to $$\{10,100,3\}$$ in BEAF, or 10 pentated to 100.[1] In tetra-tower form, it is equal to 1010...1010, with 100 tens. The term was coined by Jonathan Bowers.

This number is also called hecta-taxis (formerly hecta-teraksys) by Sbiis Saibian, and it's equal to E1#1#100 in Hyper-E Notation.[2]

Username5243 calls this number Toogol, and it's equal to 10[3]100 in Username5243's Array Notation.[3]

DeepLineMadom calls this number quidoogol, and it's equal to 10[5]100 using DeepLineMadom's Array Notation.[4]

Written out in decimal expansion, gaggol is 1 followed by $$10 \uparrow\uparrow (10 \uparrow\uparrow\uparrow 99 - 1)$$ zeroes, using Knuth's up-arrow notation.

## Approximations

Notation Approximation
Arrow Notation $$10\uparrow\uparrow\uparrow100$$ (exact)
Bird's array notation $$\{10,100,3\}$$ (exact)
Hyper-E notation $$\textrm E1\#1\#100$$ (exact)
Chained arrow notation $$10 \rightarrow 100 \rightarrow 3$$ (exact)
Hyperfactorial array notation $$102!2$$
Nested Factorial Notation $$100![3]$$
Fast-growing hierarchy $$f_4(98)$$
Hardy hierarchy $$H_{\omega^4}(100)$$
Slow-growing hierarchy $$g_{\zeta_0}(100)$$

## Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2015-03-18.
3. Username5243. Shortened listMy Large Numbers. Retrieved 2017-05-02.
4. DeepLineMadom's googology - Numbers I've coined (Retrieved 4 May 2022)

Googol and related numbers

Originals: googol · googolplex
Cockburn's examples: gargoogolplex · fzgoogolplex · (mega)fugagoogolplex
Googol-n-plex: googolduplex · googoltriplex · -quadriplex · -quinplex · -sextiplex · -septiplex · -octiplex · -noniplex · -deciplex · -centiplex
Googol-103n-plex: googolmilliplex · -megaplex · -gigaplex · -teraplex · -petaplex · -exaplex · -zettaplex · -yottaplex · -xennaplex · -vekaplex · -mekaplex
Bowers' extensions: giggol · gaggol · geegol · boogol · biggol · troogol · goobol · more...
Saibian's extensions: googol-minutia · googolchime · googoltoll · googolgong · grangol · greagol · gigangol · gugold · graatagold · gugolthra · throogol · godgahlah · tethrathoth · more...
Miscellany: googolbang (10100!) · googolminex (10^-10100) · googolteen · googolty · great googol(plex) · gooprol · little googol/googolbit · zootzootplex

Jonathan Bowers' googol series

Googol series: googol(plex/duplex/triplex/quadraplex/quinplex) · giggol(plex/duplex) · gaggol(plex/duplex) · geegol(plex) · gigol(plex) · goggol(plex) · gagol(plex)
Boogol series: boogol(plex/duplex/triplex) · biggol(plex/duplex) · baggol(plex) · beegol(plex) · bigol · boggol · bagol
Troogol series: troogol(plex/duplex) · triggol(plex/duplex) · traggol(plex/duplex) · treegol · trigol · troggol · tragol
Quintoogol series: quintoogol(plex) · quintiggol · quintaggol · quinteegol · quintigol · quintagol
Sextoogol series: sextoogol · septoogol · octoogol
Goobol series: goobol(plex) · gibbol · gabbol · geebol · gibol · gobbol · gabol
Boobol series: boobol · bibbol · babbol · beebol · bibol · bobbol · babol
Troobol series: troobol · tribbol · trabbol
Gootrol series: gootrol · gitrol · gatrol · geetrol · gietrol · gotrol · gaitrol
Bootrol series: bootrol · trootrol · quadrootrol
Gossol series: gossol(plex) · gissol · gassol · geesol(plex) · gussol
Mossol series: mossol(plex) · missol · massol · meesol · mussol
Bossol series: bossol · bissol · bassol · beesol · bussol
Trossol series: trossol · trissol · trassol · treesol · trussol · (quadrossol · quintossol)
Dubol series: dubol · dutrol · duquadrol · dossol(plex)

Googol — Greagol
Greagol — Gugold
Throogol — Godgahlah-ex-grand godgahlah

Higher basic series
2-entry series
Linear series
Two-row series

Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = $$a \uparrow^c b$$ in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.