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]
Aarex Tiaokhiao called this number gurea and it is equal to s(10,100,1,2) = s(10,10,100,1) = s(10,10,100) in strong array notation.[3]
Contents
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:
- \(a_1 = 10\)
- \(a_2 = \{10,10,99\}\)
- \(a_3 = \{10,a_2,99\}\)
- \(a_4 = \{10,a_3,99\}\)
- 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 | \(g_{\varphi(99,0)}(100)\) |
Pronunciation
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
- ↑ Username5243. shortened list - My Large Numbers. Retrieved March 2017.
- ↑ Tiaokhiao, Aarex. Aarex's Googology - SAN. Retrieved May 2020.
See also
Googol-n-plex: googol · googolplex · 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 · goobol · more...
Saibian's extensions: googolgong · grangol · greagol · gigangol · more...
Cockburn's extensions: gargoogolplex · fzgoogolplex · fugagoogolplex
Miscellany: googolteen · googolty · great googol(plex) · googolbang · zootzoot · zootzootplex · zootzootzootplex
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)
Quadroogol series: quadroogol(plex) · quadriggol(plex) · quadraggol · quadreegol · quadrigol · quadroggol · quadragol
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 · treebol · tribol · trobbol · trabol
Quadroobol series: quadroobol · quadribbol · quadrabbol · quadreebol · quadribol · quadrobbol · quadrabol · (quintoobol)
Gootrol series: gootrol · gitrol · gatrol · geetrol · gietrol · gotrol · gaitrol
Bootrol series: bootrol · trootrol · quadrootrol · (gooquadrol · booquadrol · trooquadrol · quadrooquadrol · quadreequadrol · gooquintol)
Gossol series: gossol(plex) · gissol(plex) · gassol(plex) · geesol(plex) · gussol(plex)
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)
