A fast-growing hierarchy (FGH) is a certain hierarchy mapping ordinals \(\alpha < \mu\) to functions \(f_\alpha: \mathbb{N} ightarrow \mathbb{N}\). For large ordinals \(\alpha\), \(f_\alpha\) grows very rapidly. Due to its simple and clear definition, as well as its origins in professional mathematics, FGH is a popular benchmark for large number functions. If you are unfamiliar with using ordinals in functions, you may want to read the introduction to the fast-growing hierarchy article.