Googolduplex in zeroes
Googolduplex[1] is a number equal to \(10^{10^{10^{100}}}\), or 1 followed by a googolplex zeroes. In Hyper-E notation, it is equal to E100#3.
The number has many alternative names such as googolplexplex[2], googolplusplex[3], gargoogolplex[4], googolduplex[5], googolplex2[5], and googolplexian[6].
Ten to the power of googolduplex, \(10^{10^{10^{10^{100}}}}\), is called googoltriplex.
Etymology
After backforming the "-plex" suffix from "googolplex," the term "googolplexplex" follows naturally as double application of the suffix to googol. Googologists shortened this to "duplex," from the Greek prefix for "two," indicating that the "plex" suffix should be applied twice. "Googolplusplex," "gargoogolplex," and "googolplexian" do not appear to be of any logical etymology, other than being various mutations of googolplex.
Approximations in other notations
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(10 \uparrow 10 \uparrow 10 \uparrow 100\) (exact) |
| Chained arrow notation | \(10 \rightarrow 10^{10^{100}}\) (exact) |
| Hyper-E notation | \(E100\#3\) (exact) |
| Hyperfactorial array notation | \(((69!)!)!\) |
| BEAF | \(\{10,\{10,\{10,100\}\}\}\) (exact) |
| Fast-growing hierarchy | \(f_2(f_2(f_2(324)))\) |
| Hardy hierarchy | \(H_{\omega^23}(324)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^{\omega^2}}}}(10)\) (exact) |
See also
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
- ↑ [1]
- ↑ [2]
- ↑ Saibian, Sbiis. Plexing & The Googol Series. Retrieved January 2013.
- ↑ 5.0 5.1 http://users.skynet.be/nizgorur/very_big_numbers.htm
- ↑ Googolplexian
External links
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
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