Fast Growing Hierarchy Calculator High Quality ✅
def f(self, alpha, n, depth=0): """Compute f_alpha(n).""" if depth > self.max_recursion: return None # Recursion too deep self.steps.append((alpha, n, depth))
Even the best calculator cannot print ( f_\varepsilon_0(3) ) in decimal — but it can explain and give a comparably sized expression in up-arrow notation. That is high quality. fast growing hierarchy calculator high quality
def f(alpha, n): if alpha == 0: return n+1 val = n for _ in range(n): val = f(alpha-1, val) return val def f(self, alpha, n, depth=0): """Compute f_alpha(n)
| Ordinal ( \alpha ) | Fundamental sequence ( \alpha[n] ) | |----------------------|----------------------------------------| | ( \omega ) | ( n ) (or ( n+1 ) depending on convention) | | ( \omega + k ) | ( \omega + k-1 ) (for successor steps) | | ( \omega \cdot 2 ) | ( \omega + n ) | | ( \omega^2 ) | ( \omega \cdot n ) | | ( \omega^\omega ) | ( \omega^n ) | | ( \varepsilon_0 ) | ( \omega^\varepsilon_0[n-1] ) with ( \varepsilon_0[0] = 1 ) or ( \omega ) | | ( \zeta_0 ) | ( \varepsilon_\zeta_0[n-1] ) | | ( \Gamma_0 ) | ( \varphi(\Gamma_0[n-1], 0) ) using Veblen hierarchy | depth=0): """Compute f_alpha(n).""" if depth >