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Googolception is a salad number defined in Urban Dictionary. It is created as a joke.[1]

Original article:

Googolplexian factorial (googolplexian!) multiplied by googol divided by pi to the power of googolvundaplex (a googolplex with a "decillion-2 more plexes", taken from Googology Wiki).

Then take that number and add it to googoldecaplex factorial multiplied by googod to the power of fzgoogolplex (googol 10's and googolplex to the power of googolplex, respectively, both also taken from Googology Wiki). Next, multiply that by the number of Google search results, or g taken that day. Finally, have your most energetic friend write at least five hundred more zeros next to the number before leaving.

As an (approximate, word form when necessary) equation, it would be written out like this:

(10^{10^(10^100)})!*{10^100/π}^googolvundaplex) + googoldecaplex!*(googod^{googolplex^googolplex})*g and add ≥500 zeros

Re-writing it, we would have:

\(((10^{10^{10^{100}}})!*(\frac{10^{100}}{\pi})^{E100\#10^{33}}+(E100\#11)!*10^{10^{10^{10^{100}+100}}*101}*g)*10^{\ge500}\)

In order to estimate the size of a Googolception, we find the largest number in its definition. The Googolvundaplex (page has been deleted), which equals E100#1033 (pretty close to Googolmekaplex) is of course the largest. The other parts of this number are so vanishingly small compared to Googolvundaplex that it doesn't matter. So the number can be approximated by E100#(1033+1).

This number is actually ill-defined, since the "divide by pi" part makes the number irrational, and thus it makes no sense to add "at least 500 more 0s next to the number". But whatever.

Approximations in other notations

Due to the ill-definedness of the number, the following approximation is just an expected value.

Notation Approximation
Up-arrow notation \(100 \uparrow\uparrow 10 \uparrow 33\)
Chained arrow notation \(100 \rightarrow (10 \rightarrow 33) \rightarrow 2\)
BEAF \(\{100,\{10,33\},2\}\)
Hyperfactorial array notation \((31!)!1\)
Strong array notation \(s(57,s(10,33),2)\)
Fast-growing hierarchy \(f_3(f_2(103))\)
Hardy hierarchy \(H_{\omega^3}(H_{\omega^2}(103))\)
Slow-growing hierarchy \(g_{\varepsilon_0}(g_{\omega^{18}}(57))\)

Sources

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