As the index (the subscript) of the function increases, the rate of growth accelerates at a pace that quickly eclipses any function found in traditional physics or standard calculus. The Fundamental Rules of FGH
Communities like the Googology Wiki use FGH calculators to verify the growth rates of new functions. If you invent a function G(n) , you feed it into an FGH calculator to see if it matches ( f_ω^2(n) ) or ( f_Γ_0(n) ).
if alpha == 'w': return f"prefix -> f_n(n) ..."
) , it maps numbers so large that they describe the proof-theoretic strength of entire mathematical systems. Why Use an FGH Calculator? fast growing hierarchy calculator
The calculator must first interpret the ordinal input (e.g., ω² + ω ⋅ 3).
The Fast Growing Hierarchy Calculator is recommended for:
Understanding the Fast-Growing Hierarchy Calculator: Mapping the Limits of Large Numbers As the index (the subscript) of the function
. The hierarchy is built through three core recursive rules that describe how to handle the successor of a function, limit ordinals, and the base case. 1. The Core Mathematical Definition
f sub alpha plus 1 end-sub of n equals f sub alpha to the n-th power of n For a successor ordinal
Let’s trace a tiny example to appreciate the explosion: if alpha == 'w': return f"prefix -> f_n(n)
Eventually we obtain
In the quiet corners of recreational mathematics and theoretical computer science, a peculiar challenge exists:
: The Epsilon-zero level, which bounds the provably total functions of Peano Arithmetic and characterizes numbers like Graham's Number. Mapping Famous Large Numbers to FGH