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.
Googolplexian is also equal to "10 to the power of itself googol times".
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 | \(((69!)!)!\) |
| 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) |
PronunciationEdit
There is some debate over pronunciation of this number[7], but most feel it should be pronounced as follows:
See also Edit
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
- ↑ https://googology.wikia.com/wiki/User_blog:Alemagno12/spontaneous_question
External links 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 · 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
