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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

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.

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