Boogol

The boogol is equal to \(\{10,10,100\}\) in BEAF. 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).
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.
==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 ==
==See also==
nl:Boogol
ja:ブーゴル
zh:Boogol
Category:Numbers
Category:Numbers by Jonathan Bowers
Category:Up-arrow notation level
Category:3 entry linear
Category:Googol series
Category:BEAF
Category:2-entry series
Category:Boogol series