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Supertet

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The supertet is equal to {4,4,4,4} in BEAF.[1]. It can also be written 4{{{{4}}}}4, or 4 & 4, using the array of operator. The term was coined by Jonathan Bowers. It is decently close to a well-known combinatorial constant, Harvey Friedman's n(4).

Supertet can be computed in 3-bracket operator notation using the following process:

  • \(t_1 = 4\)
  • \(t_2 = 4 \lbrace4\lbrace4\lbrace4\rbrace^{3}\rbrace^{3}\rbrace^{3} 4\)
  • \(t_3 = 4 \lbrace4\lbrace4\cdots\lbrace4\rbrace^{3}4\rbrace^{3}\cdots\rbrace^{3}4 \) with \(t_2\) 4's from the center out.
  • \(t_4 = 4 \lbrace4\lbrace4\cdots\lbrace4\rbrace^{3}4\rbrace^{3}\cdots\rbrace^{3}4 \) with \(t_3\) 4's from the center out.
  • etc.
  • Supertet is \(t_{t_{t_{\cdots1}}}\), where \(t_{t_{t_{\cdots1}}}\), where \(t_{t_{t_{t_1}}} t's\).

Supertet is comparable to \(f_{\omega^2}(4)\) in the fast-growing hierarchy.

Supertet

Visual representation of a supertet


EtymologyEdit

The name of this number is based on the words "super" and "tetra-" (four).

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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