Fast Growing Hierarchy Calculator High Quality Page

A high‑quality FGH calculator can be extended:

A high-quality tool must handle at least these ordinals: fast growing hierarchy calculator high quality

Some advanced calculators even support Taranovsky’s notation or Rathjen’s psi function. A high‑quality FGH calculator can be extended:

class FGHCalculator:
    def __init__(self, ordinal_alpha):
        self.alpha = ordinal_alpha
def fundamental_sequence(self, limit_ordinal, n):
        # Logic for Wainer Hierarchy
        if limit_ordinal == 'w':
            return n # Finite ordinal n
        if limit_ordinal == 'w*2':
            return f"w+n"
        # ... advanced logic for epsilon_0 etc.
def calculate(self, n):
        return self._f(self.alpha, n)
def _f(self, alpha, x):
        # Base Case
        if alpha == 0:
            return x + 1
# Successor Ordinal
        if is_successor(alpha):
            # Try to derive closed form to avoid iteration stack overflow
            if alpha == 1: return x + x
            if alpha == 2: return x * (2**x)
            if alpha == 3: return tetration(x) # Symbolic Up-Arrow
# If no closed form, iterate safely with memoization
            result = x
            for _ in range(x):
                result = self._f(alpha - 1, result)
            return result
# Limit Ordinal
        else:
            next_alpha = self.fundamental_sequence(alpha, x)
            return self._f(next_alpha, x)

Represent ordinals not as integers or strings but as an algebraic data type: A high-quality tool must handle at least these ordinals:

enum Ordinal 
    Zero,
    Succ(Box<Ordinal>),
    Limit(Box<dyn Fn(u64) -> Ordinal>), // fundamental sequence
    Psi(Box<Ordinal>, Box<Ordinal>), // ψ_α(β)
    Omega, // ω
    Veblen(Box<Ordinal>, Box<Ordinal>)