User blog:Kyodaisuu/Mashimo scale

Mashimo scale is defined as

\[n = floor(M^{-1}(x))\]

where \(M(x)\) is Mashimo function. Therefore, \(M(n) \le x < M(n+1)\).

For example, Mashimo scale of \(x=10^{34}\) is calculated as \(n = floor(M^{-1}(10^{34})) = floor(3.4) = 3\). Therefore, \(10^{34}\) is a large number of Mashimo scale 3.

Here is a list of googological numbers classified with Mashimo scale.