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Supertet is equal to {4,4,4,4}, {4,4(1)2} or {4,2/2} 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). It is comparable to Sbiis Saibian's grinningoltesla-tetrexitetris.

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

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

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

Supertet

Visual representation of a supertet using extended operator notation


Etymology[]

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

Approximations[]

Notation Approximation
Hyper-E notation E4##4##4##4##5
Chained arrow notation \(4\rightarrow 4\rightarrow 4\rightarrow 4\rightarrow 4\rightarrow 5\)
Strong array notation s(4,4,5,4)
Fast-growing hierarchy \(f_{\omega^2}(4)\)
Hardy hierarchy \(H_{\omega^{\omega^2}}(4)\)
Slow-growing hierarchy \(g_{\varphi(3,\omega,0)}(4)\)

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) · diteral(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
RedBandServerYT's extensions: tridecalplex
Douglas Shamlin Jr.'s extensions: quintuperdecal · triteral · dutetradecal · quadriteral · dupentadecal · duladecal · triladecal
MultiArrest91's extensions: tritredecal · tritetradecal · sextuperdecal · septuperdecal · octuperdecal · nonuperdecal · decuperdecal · centuperdecal · milluperdecal · quadritetradecal · quintitridecal
SeveralLegend9998's extensions: corboral
XRQ CORPORATION's extensions: quintiteral · quadrilatri · quintilatri · sextilatri · septilatri · octilatri · nonilatri · decilatri
Exeen Management World's extensions: dutritet · dutetratet · dupentapent · duheptasept · duheptadecal · duoctadecal · duennadecal · grand dutritri · tritridecal · tritetradecal · quadritridecal
BAT4423's extensions: duhexadecal

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