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Megafuganine is equal to \(9\uparrow\uparrow9\) or 9 tetrated to 9 or 9 pentated to 2.[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

  1. 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 · gargoogol · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugaeleven · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten boogahundred · boogagoogol · boogagoogolplex
Gag: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex

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