Fast Growing Hierarchy Calculator High Quality ((free))

The is not just a function; it is a classification system for infinity. It assigns a growth rate to every computable function, from the humble successor function ((f_0(n) = n+1)) to the mind-shattering (f_\psi(\Omega_\omega)(n)). For the uninitiated, FGH looks like abstract notation soup. For the initiated, it is the most powerful tool ever devised to compare the uncomparable.

| Calculator | Ordinal range | Multiple hierarchies | Step visualizer | BigInt | Parser | Verdict | |------------|---------------|----------------------|-----------------|--------|--------|---------| | Googology Wiki (Javascript snippet) | ε₀ only | No | No | No | No | Low | | FGH Spreadsheet (Excel) | ω^ω only | No | No | No | No | Very Low | | PyFGH (GitHub, 2020) | Up to Γ₀ | Wainer only | Partial | Yes | Weak | Medium | | Ordinal Calculator (Koteitan’s) | Up to ψ(Ω_ω) | Buchholz & Wainer | Yes | Yes | Strong | High | | Custom Desmos FGH | < ω^2 | No | No | No | No | Low | | | Up to Rathjen’s Ψ | 5+ hierarchies | Full trace | Yes | Full | High Quality (hypothetical) | fast growing hierarchy calculator high quality

Introduction: The Need for Speed In the shadowy depths of computational googology—the study of large numbers—lies a beast unlike any other. While most people are satisfied with a million, a billion, or even a googolplex, a niche community of mathematicians and programmers chases something far more elusive: the transfinite. The is not just a function; it is

But there is a problem:

enum Ordinal Zero, Succ(Box<Ordinal>), Limit(Box<dyn Fn(u64) -> Ordinal>), // fundamental sequence Psi(Box<Ordinal>, Box<Ordinal>), // ψ_α(β) Omega, // ω Veblen(Box<Ordinal>, Box<Ordinal>) For the initiated, it is the most powerful

Currently, the best resources are scattered: Koteitan’s ordinal calculator, various GitHub gists with Buchholz, and the Googology Wiki’s reference tables. But the demand is clear from the steady trickle of forum posts: "Does anyone have a working FGH calculator that goes past ε₀?"