Hierarchy Calculator High Quality — Fast Growing

The hierarchy is built using three fundamental rules of recursion: : The base function is simple incrementation. f0(n)=n+1f sub 0 of n equals n plus 1 Successor Case : For a successor ordinal , the function is defined as the -th iterate of the previous function.

def fgh(alpha, n, limit_ordinal_fundamental=None): """ Compute f_alpha(n) with custom fundamental sequences. Args: alpha: int or callable for limit ordinals returning alpha[n] n: int >= 0 limit_ordinal_fundamental: function(alpha, n) -> alpha_n """ if alpha == 0: return n + 1 if isinstance(alpha, int): # successor result = n for _ in range(n): result = fgh(alpha - 1, result, limit_ordinal_fundamental) return result # limit ordinal if limit_ordinal_fundamental: alpha_n = limit_ordinal_fundamental(alpha, n) return fgh(alpha_n, n, limit_ordinal_fundamental) raise ValueError(f"No fundamental sequence for alpha") fast growing hierarchy calculator high quality

A high-quality tool must handle at least these ordinals: The hierarchy is built using three fundamental rules