A Fast-Growing Hierarchy (FGH) calculator is a specialized tool used to explore and estimate the values of functions that grow at nearly inconceivable rates. Unlike standard scientific calculators, these tools handle large-number functions that quickly surpass physical limits, such as the total number of atoms in the universe or Graham's number. Understanding the Fast-Growing Hierarchy
The Fast-Growing Hierarchy is an ordinal-indexed family of functions (
) used in mathematical logic and "googology" to classify growth rates. It is defined by three primary rules: Base Case: (the successor function). Successor Step: fαf sub alpha recursively Limit Step: for limit ordinals, where α[n]alpha open bracket n close bracket -th term of a fundamental sequence assigned to How an FGH Calculator Works fast growing hierarchy calculator
A calculator for this hierarchy allows users to input an ordinal index ( ) and a natural number (
) to see how the function expands. Because the actual results are often too large to display as standard digits, these calculators usually provide: Introduction to the fast-growing hierarchy | Googology Wiki A Fast-Growing Hierarchy (FGH) calculator is a specialized
A typical FGH calculator takes:
and outputs ( f_\alpha(n) ).
A serious FGH calculator (say, written in Python, Haskell, or Rust) would need:
ω^ω, ω^2 + ω, ε_0, etc.φ(1,0) for ε₀, φ(2,0) for ζ₀, φ(1,0,0) for Γ₀.+, ω^, φ).