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.
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 |
|---|---|
| Chained arrow notation | \(4\rightarrow 4\rightarrow 4\rightarrow 4\rightarrow 4\rightarrow 5\) |
| Hyper-E notation | E4##4##4##4##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[]
- ↑ Bowers, Jonathan. Infinity 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 · dimendecal · 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: grand tridecalplex · 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: grand tridecal · grand emperal · grand grand emperal · quintiteral · quadrilatri · quintilatri · sextilatri · septilatri · octilatri · nonilatri · decilatri
Exeen Management World's extensions: dutritet · dutetratet · dupentapent · duheptasept · duheptadecal · duoctadecal · duennadecal · grand dutritri · demperal · tritridecal · tritetradecal · quadritridecal
BAT4423's extension: duhexadecal
ARsygo's extensions: tritridex · tritetdex · grand tritet · grand tripent · grand dozenal · grand trihectal · grand tritriplex · great tridecal · gigantic tridecal · gorged tridecal · gulp tridecal · gasp tridecal · tetrahept · tetraoct · tetraenn · grand tetradecal · pentatet · hexatet · hexapent
TheInfinitySeeker's extensions: dutritritri