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Tritet

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Corrected Tritet

Visualization of tritet using exponentiation

The tritet is equal to \( \lbrace 4,4,4 \rbrace = 4 \lbrace4\rbrace 4 = 4\uparrow\uparrow\uparrow\uparrow4\) (4 hexated to 4) in BEAF.[1] The term was coined by Jonathan Bowers. This is the fourth Ackermann number.

Googology Wiki user Hyp cos calls this number a trientet, and it's equal to s(4,4,4), s(4,2,5), s(4,4,1,2), s(4,1,1,3), or s(4,1,1,1,2) in strong array notation. [2]

Computation Edit

Tritet can be computed in the following process:

  • \(a_1 = 4\)
  • \(a_2 = 4 \uparrow\uparrow 4 = 4 \uparrow\uparrow\uparrow 2\) (this is tritet Jr.)
  • \(a_3 = 4 \uparrow\uparrow a_2 = 4 \uparrow\uparrow\uparrow 3\)
  • \(a_4 = 4 \uparrow\uparrow a_3 = 4 \uparrow\uparrow\uparrow 4\)
  • etc.
  • Tritet is equal to \(a_{a_{a_4}}\).

Etymology Edit

The name of this number is based on tri- (three) and tetra- (four), meaning that there are 3 4's in the array.

ApproximationsEdit

Notation Approximation
Up-arrow notation \(4\uparrow\uparrow\uparrow\uparrow4\) (exact)
BEAF \(\{4,4,4\}\) (exact)
Hyper-E notation \(E(4)1\#1\#1\#4\) (exact)
Chained arrow notation \(4\rightarrow4\rightarrow4\) (exact)
Hyperfactorial array notation \(5!3\)
Fast-growing hierarchy \(f_5(3)\)
Hardy hierarchy \(H_{\omega^5}(3)\)
Slow-growing hierarchy \(g_{\varphi(3,0)}(4)\)

Sources Edit

  1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
  2. Numbers from linear array notation | Steps Toward Infinity!

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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