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 the origin of the fuga- family of prefixes, introduced by his father, Alistair Cockburn, for the purpose of discussing how kids can make up more prefixes once they learn new mathematical vocabulary.
This number is less than both \(10^{10^{101}}\) and \(10^{100}!\); in terms of doubly exponential expressions they are very close. While \(10^{10^{101}} = (10^{10^{100}})^{10}\), gargoogolplex \(= (10^{10^{100}})^{2} = 10^{2 × 10^{100}} = 10^{10^{\log 2} × 10^{100}} = 10^{10^{100.301…}}\) .
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). Sbiis Saibian has once mistakenly referred the googolplexian as gargoogolplex.[3]
Approximations[]
Notation | Lower bound | Upper bound |
---|---|---|
Arrow notation | \(100\uparrow10\uparrow(100 + \log_{10}2) \approx 100\uparrow10\uparrow~100.301 \) (exact) | |
Down-arrow notation | \(100\downarrow\downarrow51\) | |
Steinhaus-Moser Notation | 56[3][3] | 57[3][3] |
Copy notation | 1[1[101]] | 2[2[101]] |
Chained arrow notation | \(100\rightarrow(10\rightarrow100)\) | |
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 |
PlantStar's Debut Notation | [1,59] | [1,60] |
BEAF & Bird's array notation | {10,{10,~100.301}} (exact) | |
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[]
- ↑ A fuga really big numbers
- ↑ The Fz, The Fuga & The Megafuga
- ↑ [https://sites.google.com/site/pointlesslargenumberstuff/home/2/prefixesandsuffixes Saibian. Pointless Large Number Stuff (2).
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