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The boogolplex is equal to {10,10,boogol} or {10,10,{10,10,100}} in BEAF.[1] It is equal to $$10 \uparrow\uparrow ... \uparrow\uparrow10$$ in arrow notation, where there are boogol ↑'s. The term was coined by Jonathan Bowers.

### Etymology

The name of this number is based on the suffix "-plex" and the number "boogol".

### Approximations in other notations

Notation Approximation
Bird's array notation $$\{10,10,\{10,10,100\}\}$$ (exactly equal)
Hyper-E notation $$E100\#\#100\#2$$
Chained arrow notation $$10 \rightarrow 10 \rightarrow (10 \rightarrow 10 \rightarrow 100)$$ (exactly equal)
Hyperfactorial array notation $$12!(12!99)$$
Fast-growing hierarchy $$f_{\omega}(f_{\omega}(101))$$
Hardy hierarchy $$H_{(\omega^{\omega})2}(101)$$
Slow-growing hierarchy $$g_{\varphi(\varphi(99,0),0)}(100)$$

### Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.

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)