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Mouffles Monster (so named by Sbiis Saibian) is cgG64(G64).[1] It is the 20th record setting entry in the "My number is bigger!" competition.[2] It is defined using the cg(x) function defined by Conway and Guy using chained arrow notation:

\(cg(1) = 1\)
\(cg(2) = 2 \rightarrow 2\)
\(cg(3) = 3 \rightarrow 3 \rightarrow 3\)
and in general
\(cg(n) = n \rightarrow n \rightarrow n \rightarrow . . . \rightarrow n \rightarrow n \rightarrow n\) with \(n\) \(n\)'s

Mouffles Monster = cgGraham's Number(Graham's Number) - the exponent indicates iteration of the cg function. Because \(cg(n)\approx f_{\omega^2}(n)\), then Mouffles Monster is approximately \(f_{\omega^2+1}(G_{64})\) using the fast-growing hierarchy.


Notation Approximation
Fast-growing hierarchy \(f_{\omega^2+1}(G_{64})\)
Hardy hierarchy \(H_{\omega^{\omega^2+1}}(G_{64})\)

See also[]

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