Fast Growing Hierarchy Calculator ~upd~
The Fast-Growing Hierarchy (FGH) is an ordinal-indexed family of functions
6. Data structures
- Ordinal type: tree structure representing CNF: list of (exponent: Ordinal, coefficient: int).
- Fundamental-sequence function: method ordinal.fundamental(n) -> Ordinal.
- Cache: map (ordinal-serialized, n) -> Result where Result may be:
is an ordinal number. Its recursive definition is remarkably simple, yet it leads to explosive growth: fast growing hierarchy calculator
), the hierarchy uses a "fundamental sequence" to choose a specific function based on the input Formula: Standard Sequence: For the first limit ordinal , the sequence is usually 4. Code Implementation (Python Example) Ordinal type: tree structure representing CNF: list of
A proper FGH calculator would let you explore this madness with a few keystrokes. The FGH is more than just a tool for "making big numbers
if __name__ == "__main__": main()The FGH is more than just a tool for "making big numbers." In proof theory, it is used to measure the strength of mathematical systems. For example, the function fϵ0f sub epsilon sub 0
Step 2: Input the Argument
This is the
# Successor Ordinal: f_alpha+1(n) = f_alpha^n(n) if isinstance(alpha, int) and alpha >= 0: # Iterate the function 'n' times result = n for _ in range(n): result = self._f(alpha - 1, result) return resultnin ( f_α(n) ). Usually,nis between 0 and 10. (Note: Forn=0orn=1, many functions collapse to tiny numbers.)