A fugagargoogolplex is the result of repeatedly exponentiating gargoogolplex a gargoogolplex times. This is the largest number mentioned by Alistair Cockburn on his A fuga really big numbers blog, and is thus the largest official number of the fuga- series. Alistair also noted that his son, Kieran, might say out this number after being introduced to the fuga- prefix.
The name is formed by applying the fuga- suffix to gargoogolplex, where fuga- means "n to the power of n to the power of n and so on, n times" and gar- turns out to simply be the square of the number. He predicted that Kieran will top fugagoogolplex with fugagargoogolplex instead.
After disambiguating from megafuga-, the fugagargoogolplex is equal to gargoogolplexgargoogolplexgargoogolplex-1 It is therefore \(\text{gargoogolplex} \downarrow\downarrow \text{gargoogolplex}\) in down-arrow notation.[1][2]
In exponential notation, it is exactly \(10^{10^{10^{10^{x}+x}+x-10^{x}}}\) where \(x = 100 + \log 2\); it is closely approximated by the quadruply exponential expression \(10^{10^{10^{10^{100.301}}}}\).
Approximation[]
| Notation | Lower bound |
|---|---|
| Down-arrow notation | \( \text{gargoogolplex} \downarrow\downarrow\text{gargoogolplex} \) |
| Arrow notation | \( \text{gargoogolplex} \uparrow \text{gargoogolplex} \uparrow ( \text{gargoogolplex} -1)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{ \text{gargoogolplex} - 1 } } } ( \text{gargoogolplex} )\) |
See also[]
- megafugagargoogolplex, the other possible intended value.
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
Sources[]
- ↑ Cockburn, Alistair. A fuga really big numbers (archived 2016.
- ↑ Cookiefonster. 2.5A. Googological prefixes and suffixes - Pointless Large Number Stuff. Retrieved 2021-07-24.