Fast Growing Hierarchy Calculator – Confirmed & Proven

The calculator allows users to input a value for the level of the hierarchy and the specific function they wish to evaluate. It then computes and displays the result. The calculator supports a range of functions, including:

Beyond being a tool for googologists, the FGH has profound implications in mathematical logic and proof theory. It provides a way to measure the strength of formal systems: the smallest ordinal (\alpha) such that the function (f_\alpha) is not provably total in a given system is a measure of that system's proof-theoretic strength. For example, the well-ordering of (\varepsilon_0) is provable in Peano arithmetic, and the function (f_\varepsilon_0) corresponds to the growth rate of Goodstein sequences. fast growing hierarchy calculator

This is a simple increment function. It merely adds 1 to the input. The calculator allows users to input a value