@lru_cache(maxsize=None) def f(alpha, n): if n == 0: return 0 # or 1, depending on convention if alpha == 0: return n + 1 if is_successor(alpha): pred = predecessor(alpha) # iterate n times result = n for _ in range(n): result = f(pred, result) return result else: # limit return f(fund(alpha, n), n)
[Insert link to calculator or provide instructions on how to access it]
: Such a calculator can serve as an educational tool, helping students understand the concepts of growth rates and computability. fast growing hierarchy calculator high quality
For limit ordinals ( \lambda ), the calculator needs a :
While standalone desktop applications are rare, several high-quality web-based and programmed resources exist: @lru_cache(maxsize=None) def f(alpha, n): if n == 0:
The Fast-Growing Hierarchy (FGH) is an ordinal-indexed family of functions used in mathematical logic and "googology" to classify the growth rates of extremely large numbers Online Fast-Growing Hierarchy Calculators
Are you trying to approximate a specific large number like or TREE(3) ? Share public link @lru_cache(maxsize=None) def f(alpha
While fully custom FGH calculators are rare due to the complexity of transfinite arithmetic, several elite resources stand out for googologists and math enthusiasts.