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)


There is some debate over pronunciation of this number[7], but most feel it should be pronounced as follows:


See also Edit

Sources Edit

  1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
  2. [1]
  3. [2]
  4. Saibian, SbiisPlexing & The Googol Series. Retrieved January 2013.
  5. 5.0 5.1
  6. Googolplexian

External links Edit

Googol and related numbers

Googol plex bang stack numbers

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