Fast Growing Hierarchy Calculator File

# Limit ordinal (assume alpha is string like 'w', 'w+1') # This is a massive simplification for demonstration

If you did compute ( f_\omega+1(4) ) as an integer, you’d need more than ( 10^100 ) bits of memory—physically impossible. Hence any honest FGH calculator never expands to a full integer; it stays in a compressed symbolic form unless the result is tiny.

For ordinals beyond a certain recursive bound, the question “Is this ordinal a limit ordinal?” can be undecidable. Real calculators restrict to and explicit fundamental sequences. fast growing hierarchy calculator

Would you like a mock UI layout or a code skeleton (Python/JS) for the core reduction engine?

So go ahead. Try to build one. Start with ( f_0(n) = n+1 ), add recursion, add ordinals, and watch your screen slowly—or not so slowly—descend into mathematical madness. # Limit ordinal (assume alpha is string like

grows, the rate of acceleration of the function increases exponentially, superseding standard arithmetic operations. The Fundamental Rules

Measuring the computational complexity of non-primitive recursive algorithms. Try to build one

An interactive tool that computes values of the fast-growing hierarchy ( f_\alpha(n) ) for user-provided ordinal ( \alpha ) (up to a reasonable limit, e.g., ( \Gamma_0 ) or less) and integer ( n ), with step-by-step expansion visualization.

The Fast-Growing Hierarchy is an indexed family of functions

Despite the difficulties, several open‑source projects have tackled the FGH: