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Googoltriplex

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Googoltriplex[1] (also known as googolplexplexplex[2], googolplusplexplus[3], googolplexianite[4]
Googoltriplex

Googoltriplex in zeroes

or gargantugoogolplex[5]) is a number equal to \(10^{10^{10^{10^{100}}}}\), or 1 followed by googolduplex zeroes. In Hyper-E Notation in can be written E100#4. In down-arrow notation it can also be written \(10 \downarrow\downarrow ((10\downarrow\downarrow101)+1)\).

Etymology Edit

The Greek prefix "tri-" (3) is understood to iterate the "-plex" suffix three times, forming an abbreviation for the unwieldy "googolplexplexplex." None of the other names seem to have any logical etymology.

Approximations in other notations Edit

Notation Approximation
Up-arrow notation \(10 \uparrow 10 \uparrow 10 \uparrow 10 \uparrow 100\) (exact)
Chained arrow notation \(10 \rightarrow 10^{10^{10^{100}}}\) (exact)
Hyper-E notation \(E100\#4\) (exact)
Hyperfactorial array notation \((((69!)!)!)!\)
BEAF \(\{10,\{10,\{10,\{10,100\}\}\}\}\) (exact)
Fast-growing hierarchy \(f_2(f_2(f_2(f_2(324))))\)
Hardy hierarchy \(H_{\omega^24}(324)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^{\omega^{\omega^2}}}}}(10)\) (exact)

Sources Edit

  1. Googology
  2. [1]
  3. [2]
  4. [3]
  5. Plexing & The Googol Series - Large Numbers by Sbiis Saibian

See also Edit

Googol and related numbers

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

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