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A googolplex expressed in factorial form?

  1. Feb 6, 2016 #1
    Does anybody know what the factorial form of a googolplex would be?
     
  2. jcsd
  3. Feb 6, 2016 #2

    Mentallic

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    Homework Helper

    So you're asking to calculate the inverse gamma function, since the gamma function and the factorial are closely related. i.e. you want to solve for n in
    [tex]n!=10^{10^{100}}[/tex]

    I can give you a quick start on the approximate magnitude of n. Since a crude approximation is [itex]n!\approx n^n[/itex], then choosing [itex]n=10^{100}[/itex] gives us
    [tex]n^n=\left(10^{100}\right)^{\left(10^{100}\right)}=10^{100\times 10^{100}}=10^{10^{102}}\approx 10^{10^{100}}[/tex]

    hence n is somewhere in the ballpark of a googol.

    Unless of course, you meant something else by your OP. Maybe you were asking what [tex]10^{10^{100}}![/tex] is?
     
  4. Feb 6, 2016 #3
    Yes I was asking what 'n' would have been, and thank you for helping.
     
  5. Feb 6, 2016 #4
    I tried to get Wolfram Alpha to solve but it exceeded the standard calculation time - maybe someone with a pro account can try it.

    Anyway just through guessing I managed to get 102483838377090000000000000000000000000000000000000000000000000000000000000000000000000000000000000! (1.0248383837709e+98!) as an answer.
     
    Last edited: Feb 6, 2016
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