Whether you are a student trying to understand ( f_\omega(100) ) or a researcher comparing proof-theoretic ordinals, demand a tool that is accurate, transparent, and powerful. Seek out — or help build — the high-quality FGH calculator that googology deserves.
: Developed by weee50, this tool uses the ExpantaNum.js library to handle functions like the Hardy Hierarchy , which is closely related to the FGH. fast growing hierarchy calculator high quality
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>) Whether you are a student trying to understand
Because many users come to FGH to learn, a "high quality" tool includes: The hybrid produced the richest outcomes—but only if
The Calculator’s final insight was subtle. Fast growth alone was seductive, but fragile; unconstrained expansion created many winners and many ghosts. Rigid hierarchy alone was reliable, but rarely revolutionary. The hybrid produced the richest outcomes—but only if the alternation was timed to the environment. In stable times, more constraint; in turbulence, broader expansion. Beyond strategies, the device taught patience with cycles: growth happens not as continuous ascent but in pulses, each pulse reshaping what comes next.
[ \beginalign f_0(n) &= n + 1 \ f_\alpha+1(n) &= f_\alpha^n(n) \quad \text(iteration) \ f_\lambda(n) &= f_\lambda[n](n) \quad \textfor limit \lambda \endalign ]
