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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 $$E1\#1\#1\#100\#2$$ (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.
2. Part 1 (LAN) - Aarex Googology

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)