Mag is a function devised by Alistair Cockburn (of fuga- glory) in one of his forum pages, considering how a five-year-old might extend gag by indicating repeated application after learning this function. \(Mag(n\) is defined as \(\underbrace{\mathrm{gag}(\mathrm{gag}(\mathrm{gag}(\mathrm{gag}(\ldots n\ldots))))}_n\), using the gag function.[1] He also never used mag (along with gag) as a prefix despite rumors of him doing so; the prefix form was coined by Sbiis Saibian, also known for coining booga-[2].
It is comparable to \(f_{\omega + 1}(n)\) in the fast growing hierarchy. Notably, \(mag(64) > g_{64}\) where \(g_{64}\) is Graham's number.
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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