| 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. | ✔ |
| Feature | Why it matters | |---------|----------------| | Step-by-step expansion | Shows ( f_\omega+2(3) \to f_\omega+1^3(3) \to \dots ) | | Ordinal normalization | Converts ( \omega+\omega+1 ) to ( \omega\cdot 2+1 ) | | Comparison of ordinals | Determines if ( \alpha < \beta ) for correct FS lookup | | Customizable FS choice | Options: Wainer (for ( < \varepsilon_0 )), Veblen, Buchholz, Madore, etc. | | LaTeX / plaintext output | Renders readable formulas | | Performance guard | Prevents infinite recursion or huge intermediate values | | Limit ordinal detection | Parses e.g. ( \omega^\omega^\omega ), ( \varepsilon_0 ), ( \Gamma_0 ) correctly | fast growing hierarchy calculator high quality
What specific features define a high-quality fast growing hierarchy calculator? | Requirement | Status for high‑quality impl |