Fast Growing Hierarchy Calculator Online

Imagine an open-source web app with:

This would be the Large Number Enthusiast’s slide rule—a window into the abyss of fast-growing functions.

Press "Expand" or "Compute."

To truly understand the tool, you should build a simple version. This handles only the Wainer hierarchy below ε₀.

def fgh(alpha, n):
    """Basic Fast Growing Hierarchy Calculator (Wainer)"""
    if n == 0:
        return 0  # Convention for f_a(0)
if isinstance(alpha, int):  # Finite ordinal
    if alpha == 0:
        return n + 1
    else:
        result = n
        for _ in range(n):
            result = fgh(alpha - 1, result)
        return result
# Limit ordinal (assume alpha is string like 'w', 'w+1')
# This is a massive simplification for demonstration
if alpha == 'w':
    return fgh(n, n)  # f_w(n) = f_n(n)
# Add logic for w+1, w*2, etc.

print(fgh(2, 3))  # Output: 24
print(fgh('w', 2)) # Output: fgh(2,2) = 8
 fast growing hierarchy calculator

Note: A production calculator requires ordinal class systems and fundamental sequence dictionaries. User-selectable fundamental sequence variants (e

Provide a concise report describing a fast-growing hierarchy calculator: definition, supported functions, algorithmic approach, limitations, example outputs, and implementation outline.