The representation of trilatri-array. Here the yellow brackets separate 3-D arrays from 3-D arrays. Call this array A. Now red brackets separate A-arrays from A-arrays. The resulting array contains 3^9 = 19683 entries.
The trilatri is equal to \(\{3,3 (3,2) 2\}\) or \(\{3,3 (0,3) 2\}\) or \(\{3,3 (0,0,1) 2\}\) in BEAF.[1] The term was coined by Jonathan Bowers. Using the array of (&) operator, it can be written \(X^{3X}\ \&\ 3\) or \(X^{X^2}\), where X evaluated as 3.
Approximations
| Notation | Approximation |
|---|---|
| Bird's Array Notation | \(\{3,3[1,1,2]2\}\) |
| Cascading-E notation | \(E(3)3\#\text{^}\#\text{^}\#\#3\) |
| Hyperfactorial Array Notation | \(3![1,[1,[1,2,2],1,2],1,3]\) |
| Fast-growing hierarchy (using CNF's fundamental sequences) | \(f_{\omega^{\omega^{\omega^2}}}(3)\) |
| Hardy hierarchy | \(H_{\omega^{\omega^{\omega^{\omega^2}}}}(3)\) |
| Slow-growing hierarchy | \(g_{\vartheta(\Omega^{\Omega^{\Omega\omega}})}(3)\) |
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
See also
Tritri series: tritri · tritet · tripent · trisept · tridecal · grand tridecal
Tetratri series: tetratri · supertet · general(plex)
Pentatri series: pentatri · superpent · pentadecal(plex)
Hexatri series: hexatri · superhex · hexadecal(plex)
Heptatri series: heptatri · supersept · heptadecal
Iteral series: superoct · octadecal · superenn · ennadecal · iteral · ultatri
Dupertri series: dupertri · duperdecal · truperdecal · quadruperdecal
Latri series: latri · emperal(plex) · hyperal(plex) · admiral
Dutritri series: dutritri · dutridecal
Dimentri series: dimentri · dulatri · trilatri · trimentri
Triakulus series: triakulus · tridecatrix
Big boowa series: big boowa · great big boowa · grand boowa
Tiaokhiao's extensions: trihex · trioct · triennet · triundecal · tridodecal · tritriplex · tritriplexian · grand tritri · tetrapent · tetrahex · grand tetratri · octatri · enneatri · decatri · undecatri · dodecatri
