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The troogolduplex is equal to {10,10,10,troogolplex} in BEAF.[1] The term was coined by Chris Bird.

Etymology

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

Approximations

Notation Approximation
Bird's array notation $$\{10,10,10,\{10,10,10,\{10,10,10,100\}\}\}$$ (exactly equal)
Hyper-E notation $$E100\#\#\#100\#3$$
Chained arrow notation $$100 \rightarrow_2 (100 \rightarrow_2 (100 \rightarrow_2 100))$$
Fast-growing hierarchy $$f_{\omega^2}(f_{\omega^2}(f_{\omega^2}(100)))$$
Hardy hierarchy $$H_{(\omega^{\omega^2}) 3}(100)$$
Slow-growing hierarchy $$g_{\varphi(99,\varphi(99,\varphi(99,99,0),0),0)}(100)$$

Sources

1. Bowers, JonathanSize 4 Arrays. Retrieved March 2014.

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)