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Can you find 0!

  1. Nov 21, 2013 #1
    can u give me the method to find the factorial of zero ?
     
  2. jcsd
  3. Nov 21, 2013 #2

    Borek

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    Staff: Mentor

    What is the definition of the factorial?
     
  4. Nov 21, 2013 #3
    [itex]0!=\Gamma(1)=\intop_{0}^{\infty} t^{1-1}\exp(-t)\mathrm{d}t=-[\exp(-t)]_{0}^{\infty}=-(0-1)=1.[/itex]

    Alternatively, there's exactly one way to arrange an empty set.
     
  5. Nov 21, 2013 #4

    Mentallic

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    Homework Helper

    I highly doubt the OP would be able to make heads or tails of this.

    [tex]n! = n(n-1)![/tex]

    Work with this definition, it's all you need.
     
  6. Nov 21, 2013 #5

    HallsofIvy

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    So your answer to the original question is that [itex]0!= 0(-1)![/itex]? But what is (-1)!?

    (Yes, you can write that 1!= 1(0!) and, if you know that 1!= 1, then it follows that 0!= 1. But better is just to state the basic definition of n! that asserts 0!= 1 for as part of the definition.)
     
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