Fast Growing Hierarchy Calculator

If you want to dive deeper, explore the Wikipedia article on the fast‑growing hierarchy for the formal definitions, the Googology Wiki for comparisons to other notations, or simply run one of the GitHub implementations mentioned above and see how far your computer can go before the numbers become too large to print.

class FGHCalculator { constructor() this.memo = new Map();

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Determining the strength of axiomatic systems by finding their proof-theoretic ordinals.

This famously huge number cannot be expressed with simple power towers. It grows at roughly the rate of If you want to dive deeper, explore the

is an ordinal. The standard definition (often using the Wainer hierarchy convention) starts with a base function and builds upward through three rules: f0(n)=n+1f sub 0 of n equals n plus 1 This is simple successor addition. Successor Ordinals:

function eval(ordinal α, int n, limits): if α == 0: return n+1 if α is successor β+1: return iterate(eval(β, ·), n, n, limits) if α is limit: λn = fundamental_sequence(α, n) return eval(λn, n, limits) If you share with third parties, their policies apply

Getting this right for ordinals like ( \omega_1^\textCK ) (the Church-Kleene ordinal) is impossible to compute fully—so practical calculators stop at ( \Gamma_0 ) or the small Veblen ordinal.

When the hierarchy reaches an infinite ordinal (a level that has no immediate predecessor, like

High-quality calculators translate FGH levels into alternative large number notations, such as Conway Chained Arrows, Bowers Exploding Array Notation (BEAF), or the Ackermann function. Applications of FGH Calculators