Fast Growing Hierarchy Calculator High Quality May 2026

The Fast-Growing Hierarchy (FGH) is a mathematical "measuring stick" used to rank the growth of functions that produce unbelievably large numbers. At its core, the FGH is an ordinal-indexed family of functions fαf sub alpha

The Fast-Growing Hierarchy Calculator: A Complete Guide

1. What is the Fast-Growing Hierarchy?

The fast-growing hierarchy is a family of functions ( f_\alpha: \mathbbN \to \mathbbN ) indexed by ordinals ( \alpha ). It is used to classify the growth rates of computable functions and to illustrate the power of ordinal notations. fast growing hierarchy calculator high quality

  1. Variants and equivalences

Fast-growing Hierarchy Calculator Prototype * Created May 2, 2023. * Last updated May 2, 2023. * Published May 2, 2023. Berkeley Snap! Variants and equivalences

To calculate or visualize the Fast-Growing Hierarchy ( FGHcap F cap G cap H Fast-growing Hierarchy Calculator Prototype * Created May 2,

  • F_ω(n) = F_n(n): produces Ackermann-like behavior surpassing any fixed finite stage.
  • Sketch: F_ω+1, F_ω·2, F_ω^2, … escalate through fast towers indexed by ordinal arithmetic; F_ε0 outruns all primitive-recursive functions provably total in PA.

    • Ordinal Calculator and Explorer: An advanced tool that explores ordinals up to Rathjen's and includes an FGH calculation mode. High-Quality Educational Guides

    import sys
from functools import lru_cache


  • Example: computing F_2(3)