The is a mathematical "measuring stick" used to rank the growth of functions that produce unbelievably large numbers. At its core, the FGH is an ordinal-indexed family of functions fαf sub alpha
| Requirement | Status for high‑quality impl | | --- | --- | | Handle α=0 | ✔ | | Handle successor α | ✔ | | Handle limit α | ✔ (needs correct fundamental seq) | | Handle n=0 | Decide (0 or 1) | | Prevent infinite recursion | ✔ by limiting α descent | | Show exact results for small n | ✔ | | Show approx for large n | ✔ (Knuth up‑arrows, Hyper‑E) | | Accept CNF string input | ✔ | | Output in readable ordinal notation | ✔ | | Unit tests: f_ω(3)=8, f_ω+1(3)=2048 etc. | ✔ | fast growing hierarchy calculator high quality
. A high-quality calculator allows you to toggle between different standard systems (like the Wainer hierarchy). 3. Big Number Notation Translation # Successor Ordinal if is_successor(alpha): # Try to
is_zero, is_successor, is_limitfundamental_sequence(n)add, multiply, exponentiate (using normal form)# Successor Ordinal if is_successor(alpha): # Try to derive closed form to avoid iteration stack overflow if alpha == 1: return x + x if alpha == 2: return x * (2**x) if alpha == 3: return tetration(x) # Symbolic Up-Arrow is_limit fundamental_sequence(n) add