Googolduplex in zeroes
Googolduplex is a number equal to \(10^{10^{10^{100}}}\), or 1 followed by a googolplex zeroes.[1] In Hyper-E notation, it is equal to E100#3. It is 1010100+1 digits long.
The number has many alternative names such as googolplexplex,[2] googolplusplex,[3] gargoogolplex,[4] googolduplex,[5] googolplex2,[5] and googolplexian.[6]
Writing down the full decimal expansion would take 1010100-6 books of 400 pages each, with 2,500 digits on each page.
Ten to the power of googolduplex, \(10^{10^{10^{10^{100}}}}\), is called googoltriplex.
Googolduplex is also equal to "10 to the power of itself googol times".
Etymology
After back-forming 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. The names "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) |
Pronunciation
There is some debate over pronunciation of this number,[7] but most feel it should be pronounced as follows:
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
- ↑ https://googology.wikia.com/wiki/User_blog:Alemagno12/spontaneous_question
External links
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
