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The geegolplex is equal to {10,geegol,4} in BEAF.[1] The term was coined by Jonathan Bowers. In the up-arrow notation it can be written as \(10 \uparrow\uparrow\uparrow\uparrow \text{geegol}\).

Geegolplex is equal to E1#1#1#100#2 = E1#1#1#100#(E1#1#1#100) = E1#1#1#geegol in Hyper-E notation.

Aarex Tiaokhiao calls this number geegolquadrex.[2]

Etymology[]

The name of the number is based on suffix -plex and the number geegol.

Approximations[]

Notation Approximation
Hyper-E notation \(\textrm{E}1\#1\#1\#100\#2\) (exact)
Chained arrow notation \(10 \rightarrow (10 \rightarrow 100 \rightarrow 4) \rightarrow 4\) (exact)
Hyperfactorial array notation \((102!3)!3\)
Fast-growing hierarchy \(f_5(f_5(100))\)
Hardy hierarchy \(H_{(\omega^5) 2}(100)\)
Slow-growing hierarchy \(g_{\eta_{\eta_0}}(100)\)

Sources[]

See also[]

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
Quadroogol series: quadroogol(plex/duplex) · quadriggol(plex) · quadraggol · quadreegol · quadrigol · quadroggol · quadragol
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
Quadroobol series: quadroobol · quadribbol · quadrabbol · (quintoobol)
Gootrol series: gootrol · gitrol · gatrol · geetrol · gietrol · gotrol · gaitrol
Bootrol series: bootrol · trootrol · quadrootrol
Gooquadrol series: gooquadrol · booquadrol · quadreequadrol · (gooquintol)
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)

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