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.
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1You might be interested in this: http://en.wikipedia.org/wiki/Empty_product. – Srivatsan Sep 26 '11 at 19:12
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3Possible duplicate of 25333, 25794 and 20969. – Srivatsan Sep 26 '11 at 19:14
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1I've posted a new answer to the "possible duplicate" question, and I think it's simpler than all others. – Michael Hardy Sep 26 '11 at 20:21
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Can the downvoter explain him/herself? – Srivatsan Sep 26 '11 at 22:17
1 Answers
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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.
Mark Bennet
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1Also, there's only one way to arrange zero things. :) – J. M. ain't a mathematician Sep 26 '11 at 21:42
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