Fast-Growing Hierarchy

The Fast-growing hierarchy is a function that makes use of transfinite ordinals to produce and stratify extremely large classes of numbers.

Introduction: The Basics
The basic rules of the fast-growing hierarchy are below. Note that $$f_{n}^{m}(a)$$ denotes recursion of $$f_{n}$$ m-times, $$\alpha$$ refers to a successor ordinal, and that $$\beta$$ indicates a limit ordinal; with $$\beta[n]$$ indicating the nth term in the fundamental sequence of the limit ordinal $$\beta$$.

$$f_{0}(n)=n+1$$

$$f_{\alpha}(n)={f_{\alpha-1}^{n}}(n)$$

$$f_{\beta}(n)=f_{\beta[n]}(n)$$

[Will be continued]