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The boogol is equal to $$\{10,10,100\}$$ in BEAF.[1] It is equal to $$10\underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{100}10 = 10 \uparrow^{100} 10$$ in up-arrow notation. The term was coined by Jonathan Bowers. It is comparable to gugold, woogol and hyperon.

This number is equal to $$10[0,1]100$$ in UNAN, and Username5243 calls this number a kiloogol (formerly megoogol).[2]

Aarex Tiaokhiao called this number gurea or golsol and it is equal to s(10,100,1,2) = s(10,10,100,1) = s(10,10,100) in strong array notation.[3][4]

## Etymology

The name of the number is based on Latin prefix "bi-" and the number "googol".

## Computation

Boogol can be computed in the following process:

• $$a_1 = 10$$
• $$a_2 = \{10,10,99\}$$ - Boogolchunk
• $$a_3 = \{10,a_2,99\}$$
• $$a_4 = \{10,a_3,99\}$$
• etc.
• Boogol is equal to $$a_{10}$$.

## Approximations in other notations

Notation Approximation
Bird's array notation $$\{10,10,100\}$$ (exact)
Graham Array Notation $$[10,10,100]$$ (exact)
Hyper-E notation $$E10\#\#100$$
Chained arrow notation $$10 \rightarrow 10 \rightarrow 100$$ (exact)
Hyperfactorial array notation $$12!99$$
Fast-growing hierarchy $$f_{101}(9)$$
Hardy hierarchy $$H_{\omega^{101}}(9)$$
Slow-growing hierarchy $$g_{\varphi(99,0)}(100)$$

## Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Username5243. shortened list - My Large Numbers. Retrieved March 2017.
3. Tiaokhiao, Aarex. Aarex's Googology - SAN. Retrieved May 2020.
4. Tiaokhiao, Aarex. Part 1 (LAN) - Aarex's Googology (archived). Retrieved 29 October 2020.

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 · quintoggol · quintagol · (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
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)