Visualisation of trisept using exponentations.

The trisept is equal to \(\lbrace7,7,7 \rbrace\) or \(7\lbrace7\rbrace7\) (7 enneated to 7) in BEAF.[1] The term was coined by Jonathan Bowers. This is the seventh Ackermann number.

"Fashion" view of trisept using iterated power towers with arrows.

Etymology

The name of this number is based on tri- (three) and septa- (seven), meaning that there are 3 7's in the array.

Approximations

Notation Approximation
BEAF \(\{7,7,7\}\) (exact)
Up-arrow notation \(7\uparrow^{7} 7\) (exact)
Chained arrow notation \(7\rightarrow 7\rightarrow 7\) (exact)
Hyperfactorial array notation \(9!6\)
Notation Array Notation \((7\{3,3\}7)\) (exact)
Fast-growing hierarchy \(f_{8}(7)\)
Hardy hierarchy \(H_{\omega^{7}5}(7)\)
Slow-growing hierarchy \(g_{\varphi(6,0)}(7)\)

Sources

  1. Bowers, JonathanInfinity 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

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