- "Triteto" redirects here. It is not to be confused with tritet.
Visualization of grahal using exponentiation
The grahal is equal to \(g_1\) in Graham's function. The term was coined by Aarex Tiaokhiao.[1]
It is equal to \(3 \uparrow\uparrow\uparrow\uparrow 3 = 3 \uparrow\uparrow\uparrow\uparrow\uparrow 2\) in up-arrow notation.
Wiki user Hyp cos calls this number triteto, and it's equal to s(3,3,4), s(3,2,5), or s(3,4,1,2) in strong array notation. [2]
Tim Urban calls this number "NO I CAN'T EVEN" in his Wait Buy Why article "From 1,000,000 to Graham's Number".[3]
Computation[]
Grahal can be computed in the following process:
- \(a_1 = 3\)
- \(a_2 = 3^{3^3} =\) \(7,625,597,484,987\)
- \(a_3 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}\) with \(a_2\) threes = Tritri
- \(a_4 = 3^{3^{3^{.^{.^{.^{3^3}}}}}}\) with \(a_3\) threes
- etc.
- Grahal is equal to \(a_{a_3} = a_{\text{Tritri}}\).
Approximations[]
| Notation | Approximation |
|---|---|
| Arrow notation | \(3\uparrow\uparrow\uparrow\uparrow3\) (exact) \(=3\uparrow\uparrow\uparrow\uparrow\uparrow2\) |
| Bowers' Exploding Array Function | \(\{3,3,4\}\) (exact) \(=\{3,2,5\}\) |
| Chained arrow notation | \(3\rightarrow3\rightarrow4\) (exact) \(3\rightarrow2\rightarrow5\) |
| Hyper-E notation | \(\textrm E[3]1\#1\#1\#3\) (exact) |
| Hyperfactorial array notation | \(3!5\) (exact) |
| Fast-growing hierarchy | \(f_4(f_3(f_2(37)))\) |
| Hardy hierarchy | \(H_{\omega^4+\omega^3+\omega^2}(37)\) |
| Slow-growing hierarchy | \(g_{\eta_0} (3)\) |
Sources[]
See also[]
Grahal group: grahal · graham grahal
Forcal group: forcal · graham forcal · graham graham forcal · graham graham graham forcal · force forcal · force force forcal · force force force forcal
Suporcal group: suporcal · force suporcal · force force suporcal · force force force suporcal · superior suporcal · superior superior suporcal · superior superior superior suporcal
Megocal group: megocal · force megocal · superior megocal · superior superior megocal · megaior megocal · megaior megaior megocal · Megaior megaior megaior megocal
Hypercal group: hypercal · force hypercal · superior hypercal · megaior hypercal · hyperior hypercal · hyperior hyperior hypercal · hyperior hyperior hyperior hypercal
Gorgcal group: gorgcal · force gorgcal · superior gorgcal · megaior gorgcal · hyperior gorgcal · gorgcaior gorgcal · gorgcaior gorgcaior gorgcal · gorgcaior gorgcaior gorgcaior gorgcal
Gulfcal group: gulfcal · gulfcaior gulfcal · gulfcaior gulfcaior gulfcal · gulfcaior gulfcaior gulfcaior gulfcal · gaspocal · gaspocaior gaspocal · gaspocaior gaspocaior gaspocal · gaspocaior gaspocaior gaspocaior gaspocal · ginorcal · ginorcaior ginorcal · ginorcaior ginorcaior ginorcal · ginorcaior ginorcaior ginorcaior ginorcal
Terribocal group: terribocal · Terribocaior Terribocal · terribuporcal · Terribuperior Terribuporcal · terribegocal · terribypercal · terriborgecal · terribulfcal · terribaspcal · terribinorcal
Tribocal group: tribocal · Tribocaior Tribocal · tribuporcal · tribegocal · tribypercal · tetribocal · tetribuporcal · pentibocal · hexibocal · heptibocal · octibocal
Tris-Terribocal group: Tris-Terribocal · Tris-Terribocaior Tris-Terribocal · Tris-Terribuporcal · Tris-Terribegorcal · Tris-Terribypercal · Tris-Terrible-Terribocal · Tris-Terrible-Tribocal · Tris-Terrible-Tetribocal · Tris-Tribocal · Tris-Tribocaior Tris-Tribocal · Tris-Trible-Terribocal · Tris-Trible-Tribocal · Tris-Trible-Tetribocal · Tris-Tetribocal · Tris-Pentibocal · Tris-Hexibocal
Teris-Terribocal group: Teris-Terribocal · Teris-Terribuporcal · Teris-Terribegorcal · Teris-Terrible-Terribocal · Teris-Terrible-Tribocal · Teris-Terrible-Tetribocal · Teris-Terrible-Tris-Terribocal · Teris-Terrible-Tris-Tribocal · Teris-Terrible-Tris-Tetribocal · Teris-Tribocal · Teris-Tetribocal · Teris-Pentibocal
Petris-Terribocal group: Petris-Terribocal · Petris-Tribocal · Petris-Tetribocal · Ectris-Terribocal · Ectris-Tribocal · Ectris-Tetribocal · Zetris-Terribocal · Zetris-Tribocal · Zetris-Tetribocal · Yotris-Terribocal · Yotris-Tribocal · Yotris-Tetribocal
Superis-Terribocal group: Superis-Terribocal · Superis-Terribuporcal · Superis-Terribmegocal · Superis-Terribypercal
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex