Fast Growing Hierarchy Calculator [updated] ★ (FREE)

: Because (f_\alpha(n)) quickly exceeds the capacity of standard integer types, a calculator must use big‑integer arithmetic or symbolic output. For large (\alpha), the numbers are so vast that even symbolic representation (like Knuth’s up‑arrow towers) becomes unwieldy.

The hierarchy is defined by three primary rules that govern how functions evolve from basic operations into astronomically large numbers: . This is the successor function. Successor Step . The function at level -th iteration of the function at level applied to Limit Step is a limit ordinal. This process, known as diagonalization , uses the -th term of a fixed fundamental sequence assigned to 2. Common Levels and Growth Rates As the index

class FGHCalculator { constructor() this.memo = new Map(); fast growing hierarchy calculator

Whether you are looking to explore like ϵ0epsilon sub 0 , or the Bachmann-Howard ordinal.

def main(): print("--- Fast Growing Hierarchy Calculator ---") print("Valid inputs for 'alpha': 0, 1, 2, 3, ... or 'w' (omega)") print("Warning: f_3(n) grows incredibly fast. f_3(3) is huge.") print("Type 'exit' to quit.\n") : Because (f_\alpha(n)) quickly exceeds the capacity of

: Existing FGH calculators are mostly code libraries. A web‑based interface that allows the user to select an ordinal notation, input a small (n), and see the step‑by‑step expansion of (f_\alpha(n)) would be a valuable educational tool.

For programmable implementations, you can clone the source code and run the functions with small arguments. The Python fast-growing-hierarchy repository, for example, includes a simple test: for any ordinal input, fast(alpha, 2) should return 4. This is the successor function

— Tetration: Iterating powers creates towers of exponents. This level easily surpasses a Googolplex for small inputs. Entering the Transfinite (The

Provide a concise evaluator outline — pseudo-Python:

if __name__ == "__main__": main()

We can use the FGH framework to categorize exactly where famous large numbers sit on the scale of mathematical growth: