- This page is about Alistair Cockburn's definition. For the alternative definition, see Googolduplex.
The gargoogolplex is a googolplex squared, or \((10^{10^{100}})^2 = 10^{2\cdot10^{100}}.\)[1][2] It was invented by Kieran Cockburn (Alistair's son), when he said "My space commander rules a gargoogolplex stars. It is a googolplex googolplexes."
This number is less than \(10^{10^{101}}\). While gargoogolplex = \((10^{10^{100}})^{2}\), \(10^{10^{101}}\) = \((10^{10^{100}})^{10}\).
Gargoogolplex should be interpreted as gar-googolplex, not gargoogol-plex. The latter equals to \(10^{10^{200}}\), which is a lot larger than a gargoogolplex (which has been named gargoogol-plexed).
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(100\uparrow10\uparrow100\) | |
| Down-arrow notation | \(100\downarrow\downarrow51\) | |
| Steinhaus-Moser Notation | 56[3][3] | 57[3][3] |
| Copy notation | 1[1[101]] | 2[2[101]] |
| H* function | H(6H(32)) | H(7H(32)) |
| Taro's multivariable Ackermann function | A(3,A(3,331)) | A(3,A(3,332)) |
| Pound-Star Notation | #*((1))*(9,6,6,4,4)*7 | #*((1))*(0,7,6,4,4)*7 |
| BEAF | {100,{10,100}} | |
| Hyper-E notation | E[100]50#2 | |
| Bashicu matrix system | (0)(1)[18] | (0)(1)[19] |
| Hyperfactorial array notation | (69!)! | (70!)! |
| Fast-growing hierarchy | \(f_2(f_2(326))\) | \(f_2(f_2(327))\) |
| Hardy hierarchy | \(H_{\omega^22}(326)\) | \(H_{\omega^22}(327)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^2}2}}(10)\) | |
Sources
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 · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · 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