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Possible Duplicate:
Prove $0! = 1$ from first principles
Why does 0! = 1?

I was wondering why,

$0! = 1$

Can anyone please help me understand it.

Thanks.

  • 1
    You might be interested in this: http://en.wikipedia.org/wiki/Empty_product.2011-09-26
  • 3
    Possible duplicate of [25333](http://math.stackexchange.com/questions/25333/why-does-0-1), [25794](http://math.stackexchange.com/questions/25794/factorial-of-0-a-convenience) and [20969](http://math.stackexchange.com/questions/20969/prove-0-1-from-first-principles).2011-09-26
  • 1
    I've posted a new answer to the "possible duplicate" question, and I think it's simpler than all others.2011-09-26
  • 0
    Can the downvoter explain him/herself?2011-09-26

1 Answers 1

3

Answer 1: The "empty product" is (in general) taken to be 1, so that formulae are consistent without having to look over your shoulder. Take logs and it is equivalent to the empty sum being zero.

Answer 2: $(n-1)! = \frac {n!} n$ applied with $n=1$

Answer 3: Convention - for the reasons above, it works.

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    Also, there's only one way to arrange zero things. :)2011-09-26
  • 0
    @J.M. Especially thoughts ...2011-09-26