Epsilon level

This category contains numbers that can be defined or estimated using fast-growing hierarchy in the form f_α(n) with α in Cantor normal form of (iterated) epsilon numbers and reasonably small values of n, but no higher phi ordinals. The Goodstein sequence, a function that cannot be proven using Peano arithmetic, resides here.

The lower bound of this category is \(f_{\varphi(1,0)}^2(10)\) aka \(f_{\varepsilon_0}^2(10)\), and the upper bound is \(f_{\varphi(2,0)}^2(10)\) aka \(f_{\zeta_0}^2(10)\).