Fast Growing Hierarchy Calculator May 2026

Fast-Growing Hierarchy Calculator — Detailed Guide

This guide explains fast-growing hierarchies (FGHs), how to compute values at small ordinals, practical strategies for a calculator implementation, algorithms and data structures, performance considerations, and examples. It assumes familiarity with ordinals up to ε0 and basic recursion theory; if not, the worked examples will still illustrate concrete cases.

2. Choices that matter for a calculator

• Base function f0: choose n+1 (standard) or something else (e.g., n+2) — affects constants but not asymptotic hierarchy.
• Ordinal notation system: decide how far you want to support (natural numbers, ω, ω^ω, ε0, Γ0, etc.).
• Fundamental sequences: must provide a computable sequence (λ[n]) for each countable limit ordinal λ in your notation.
• Evaluation domain: inputs (n) must be small; values explode quickly — treat outputs as big integers or use growth descriptors.
• Representation of outputs: exact integers become impossible quickly; instead provide:

  Small Ordinals (0, 1, 2):

  9. Deliverables (if you want me to implement)

  • Prototype CLI in Python implementing ordinals < ε0 and evaluator with BigInt.
  • Web demo with input fields, result modes, and interactive graphs.
  • Documentation of conventions and limits.

  Key Features of a Robust Calculator

  A good FGH calculator must handle:

  The fast growing hierarchy calculator offers several advantages and applications: fast growing hierarchy calculator