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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.

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

## Etymology Edit

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

## Computation Edit

Boogol can be computed in the following process:

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

## Approximations in other notations Edit

Notation Approximation
Bird's 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 Edit

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Username5243. shortened list - My Large Numbers. Retrieved March 2017.

Jonathan Bowers' googol series

Googol series: googol(plex/duplex/triplex/quadraplex) · 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(plex) · boggol(plex) · bagol(plex)
Troogol series: troogol(plex/duplex) · triggol(plex) · traggol(plex) · treegol(plex) · trigol(plex) · troggol(plex) · tragol(plex)