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"Tetoogol" redirects here. It is not to be confused with tetroogol.

Geegol is equal to $$\{10,100,4\}$$ in BEAF, or 10 hexated to 100.[1] It can also be written as 10{4}100 in the bracket-operator notation. In up-arrow notation, this number is written as $$10 \uparrow\uparrow\uparrow\uparrow 100$$. The term was coined by Jonathan Bowers.

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

Username5243 calls this number Tetoogol, and it's equal to 10[4]100 in Username5243's Array Notation.[3]

It can be computated in the following process:

Stage 1: 10

Stage 2: 10^10^...10^10 with Stage 1 10s

Stage 3: 10^10^...10^10 with Stage 2 10s

......

Geegol is Stage Stage ...... Stage Stage 1 with 100 stages.

## Approximations

Notation Approximation
Up-arrow notation $$10 \uparrow\uparrow\uparrow\uparrow 100$$ (exact)
Bird's array notation $$\{10,100,4\}$$ (exact)
Hyper-E notation $$\textrm{E}1\#1\#1\#100$$ (exact)
Steinhaus-Moser Notation 100[6]
Chained arrow notation $$10 \rightarrow 100 \rightarrow 4$$ (exact)
Hyperfactorial array notation $$102!3$$
Strong array notation s(10,100,4) (exact)
Fast-growing hierarchy $$f_5(100)$$
Hardy hierarchy $$H_{\omega^5}(100)$$
Slow-growing hierarchy $$g_{\eta_0}(100)$$

## Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2015-04-01.
3. Username5243. Shortened listMy Large Numbers. Retrieved 2017-05-02.

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
Tetoogol · Penoogol · Exoogol · Eptoogol · Ottoogol · Ennoogol · Dekoogol
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.