Megafuganine is equal to \(9\uparrow\uparrow9\).[1] It is approximately equal to \(\textrm E369,693,100\#7\) in Hyper-E notation.
Its exact value can be simplified (sort of) with laws of algebra, just like with Tritet Jr.:
\(9\uparrow\uparrow9 = 9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}} = 9^{9^{9^{9^{9^{9^{9^{387,420,489}}}}}}} = 9^{9^{9^{9^{9^{9^{3^{774,840,978}}}}}}} = 9^{9^{9^{9^{9^{3^{2\times3^{774,840,978}}}}}}} = 9^{9^{9^{9^{3^{2\times3^{2\times3^{774,840,978}}}}}}}\)
\(= \ldots = 3^{2\times3^{2\times3^{2\times3^{3^{2\times3^{2\times3^{774,840,978}}}}}}}\)
The name is formed by adding the megafuga- prefix to 9.
Approximation[]
| Notation | Approximation |
|---|---|
| Arrow notation | \(9\uparrow\uparrow9\) |
| Fast-growing hierarchy | \(f_3(9)\) |
| Hardy hierarchy | \(H_{\omega^3}(9)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_0}(9)\) |
| Steinhaus-Moser Notation | \((9-1)[4]\) lower bound \(9[4]\) upper bound |
| Strong array notation | s(9,9,2) |
| Bowers Exploding Array Function | \(\{ 9, 9, 2\}\) |
| Bird's array notation | \(\{ 9, 9, 2\}\) |
| Hyperfactorial array notation | \(9!1\) lower bound \((9+1)!1\) upper bound |
| Chained arrow notation | \(9\rightarrow9\rightarrow 2\) |
Sources[]
- ↑ Saibian, Sbiis. 3.2.2 - The Fz, The Fuga & The Megafuga - Large Numbers. Retrieved 2017-03-10.
See also[]
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzthirty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex