Aperioexpansion refers to the binary function \(a\{\{b\}\}a\), using Bowers' extended hyper-operators.[1]. The term was coined by Aarex Tiaokhiao.
In the fast-growing hierarchy, \(f_{\omega+b}(a)\) approximately corresponds to the growth rate of aperioexpansion.
Approximations in other notations[]
| Notation | Approximation |
|---|---|
| Bowers' Exploding Array Function | \(\{a,a,b,2\}\) (exact) |
| Hyper-E notation | \(Ea\#\#a\#\#b\) |
| X-Sequence Hyper-Exponential Notation | \(a \{X+b\} a\) (exact) |
| Fast-growing hierarchy | \(f_{\omega+b}(a)\) |
| Hardy hierarchy | \(H_{\omega^{\omega+b}}(a)\) |
| Slow-growing hierarchy | \(g_{\varphi(1,b,0)}(a)\) |
Sources[]
See also[]
3 entry: undecation · doedecation · tredecation · vigintation (doe) · trigintation · centation (tri) · aperiotion (hyper)
4 entry: undeconation · doedeconation · tredeconation · aperioexpansion · aperioexplosion
5 entry: megotion (multi/power/tetra) · megoexpansion (multi/power/tetra) · megoexplosion · megodetonation · gigotion (expand/explod/deto) · terotion · petotion · hatotion · hepotion · ocotion · nanotion · uzotion · uuotion · udotion · utotion · ueotion · upotion · uhotion · uaotion · uootion · unotion · dzotion · tzotion · uzzotion
6 entry: powiaination (multi/power/tetra) · expandaination (multi/power/tetra) · explodaination · detodaination · megodaination · megoexpandaination · megoexplodaination · megodetodaination · gigodaination · terodaination · powiairiation · megodairiation · gigodairiation · terodairiation
7+ entries: heptogation · octogation · enneogation · decogation
Dimensional: iteration · cuboiteration · expoiteration · megoiteration · trioteration · tetroteration · trixxation · expotrixxation · iterotrixxation · triotixation
Legion: legislation