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Trisept

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Trisept

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.
Trisept-0

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

Etymology Edit

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

Approximations Edit

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)
Boris's sezration notation \([7,3]\) (exact)
Fast-growing hierarchy \(f_{8}(7)\)
Hardy hierarchy \(H_{\omega^{7}5}(7)\)
Slow-growing hierarchy \(g_{\varphi(6,0)}(7)\)

Sources Edit

  1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.

See also Edit

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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