A fzgoogolplex is a googolplex to the power of a googolplex = \(\text{googolplex}^{\text{googolplex}} = (10^{10^{100}})^{10^{10^{100}}} = 10^{10^{100} × 10^{10^{100}}}= 10^{10^{10^{100}+100}}\).[1][2][3][4] This number is directly mentioned by Alistair Cockburn from A fuga really big numbers as an example of how kids might name the next large number, along with fzfour (256) and fzmillion (106000000).
It is comparable to a googolduplex, even though it's actually equal to raising a googolduplex to the power of a googol. The number is extremely close to googolduplex in triply exponential standards; it can be expressed as \(10^{10^{10^{100 + R}}}\) where \(R = \log\frac{10^{100} + 100}{10^{100}} \approx 4.343 × 10^{-99}\). The triple exponent is only 44 googolth greater than the triple exponent of googolduplex.
Approximations[]
| Notation | Approximation |
|---|---|
| Arrow notation | \((10\uparrow(10\uparrow100))\uparrow\uparrow2\) (exact) |
| Fast-growing hierarchy | \(f_2^3(324)\) |
Sources[]
- ↑ Cockburn, Alistair. A fuga really big numbers (archived 2016-04-11).
- ↑ Saibian, Sbiis. The Fz, The Fuga & The Megafuga. Retrieved 2021-07-22.
- ↑ Cookiefonster. 2.5A. Googological prefixes and suffixes - Pointless Large Number Stuff. Retrieved 2021-07-22.
- ↑ Very big numbers
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
Originals: googol · googolplex
Cockburn's examples: gargoogolplex · fzgoogolplex · (mega)fugagoogolplex
Googol-n-plex: googolduplex · googoltriplex · -quadriplex · -quinplex · -sextiplex · -septiplex · -octiplex · -noniplex · -deciplex · -centiplex
Googol-103n-plex: googolmilliplex · -megaplex · -gigaplex · -teraplex · -petaplex · -exaplex · -zettaplex · -yottaplex · -xennaplex · -vekaplex · -mekaplex
Bowers' extensions: giggol · gaggol · geegol · boogol · biggol · troogol · goobol · more...
Saibian's extensions: googol-minutia · googolchime · googoltoll · googolgong · grangol · greagol · gigangol · gugold · graatagold · gugolthra · throogol · godgahlah · tethrathoth · more...
Miscellany: googolbang (10100!) · googolminex (10^-10100) · googolteen · googolty · great googol(plex) · gooprol · little googol/googolbit · zootzootplex