def fast_growing_hierarchy(n, func_num): if func_num == 1: return n + 1 elif func_num == 2: return 2 * n elif func_num == 3: return 2 ** n elif func_num == 4: return 2 ** (2 ** n) else: raise ValueError("Invalid function number")
Modern development is pushing FGH calculators into new domains:
If you are looking to specifically calculate values for large numbers, perhaps you are interested in exploring: fast growing hierarchy calculator
Direct naive recursion quickly explodes. Use these techniques:
Limit λ:
Understanding the Fast-Growing Hierarchy Calculator: Mapping the Limits of Large Numbers
The fast-growing hierarchy is a family of functions (f_\alpha: \mathbbN \rightarrow \mathbbN), where the subscript (\alpha) is a (usually large) countable . It is defined through three simple rules: AI responses may include mistakes
If you want to explore further, let me know if you would like to map a to the hierarchy, see the Python pseudo-code for a basic FGH simulator, or explore advanced transfinite ordinals . AI responses may include mistakes. Learn more Share public link
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