Googolduplex
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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 
Edit
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 Edit
| 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 | \(((70!)!)!\) |
| 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) |
Sources Edit
- ↑ 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 Edit
See also Edit
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
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 · zootzootplex
