Googoltriplex in zeroes
Googoltriplex[1] (also known as googolplexplexplex,[2] googolplusplexplus,[3] googolplexianite[4], googolplexianth[5] or gargantugoogolplex[6]) is a number equal to \(10^{10^{10^{10^{100}}}}\), or 1 followed by googolduplex zeroes. In Hyper-E Notation it can be written as E100#4. In down-arrow notation it can also be written \(10 \downarrow\downarrow ((10\downarrow\downarrow101)+1)\). It is 101010100+1 digits long.
Writing down the full decimal expansion would take 101010100-6 books of 400 pages each, with 2,500 digits on each page (except for the first, which would have 2,501).
Etymology
The Greek prefix "tri-" (3) is understood to iterate the "-plex" suffix three times, forming an abbreviation for the unwieldy "googolplexplexplex." None of the other names seem to have any logical etymology.
Approximations in other notations
| Notation | Approximation |
|---|---|
| Arrow notation | \(10 \uparrow 10 \uparrow 10 \uparrow 10 \uparrow 100\) (exact) |
| Chained arrow notation | \(10 \rightarrow (10 \rightarrow (10 \rightarrow (10 \rightarrow 100)))\) (exact) |
| Hyper-E notation | \(E100\#4\) (exact) |
| Hyperfactorial array notation | \((((69!)!)!)!\) |
| BEAF | \(\{10,\{10,\{10,\{10,100\}\}\}\}\) (exact) |
| Fast-growing hierarchy | \(f_2^{4}(326)\) |
| Hardy hierarchy | \(H_{\omega^2\times 4}(326)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^{\omega^{\omega^2}}}}}(10)\) (exact) |
Sources
See also
Googol-n-plex: googol · googolplex · 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 · goobol · more...
Saibian's extensions: googolgong · grangol · greagol · gigangol · more...
Cockburn's extensions: gargoogolplex · fzgoogolplex · fugagoogolplex
Miscellany: googolteen · googolty · great googol(plex) · googolbang · zootzoot · zootzootplex · zootzootzootplex
0-stack series: googol · googolplex · googolbang · googolplexplex · googolplexbang · googolbangplex · googolbangbang · googolplexplexplex · googolplexplexbang · googolplexbangplex · googolplexbangbang · googolbangplexplex · googolbangplexbang · googolbangbangplex · googolbangbangbang
1-stack series: googolstack · googolstackplex · googolstackbang · googolstackplexplex · googolstackplexbang · googolstackbangplex · googolstackbangbang · googolplexstack · googolplexstackplex · googolplexstackbang · googolbangstack · googolbangstackplex · googolbangstackbang · googolplexplexstack · googolplexbangstack · googolbangplexstack · googolbangbangstack
2-stack series: googolstackstack · googolstackstackplex · googolstackstackbang · googolstackplexstack · googolstackbangstack · googolplexstackstack · googolbangstackstack
3-stack series: googolstackstackstack
