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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.


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marked as duplicate by Srivatsan, mixedmath, Rahul, Brian M. Scott, yunone Sep 26 '11 at 19:21

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

You might be interested in this: – Srivatsan Sep 26 '11 at 19:12
Possible duplicate of 25333, 25794 and 20969. – Srivatsan Sep 26 '11 at 19:14
I'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
Can the downvoter explain him/herself? – Srivatsan Sep 26 '11 at 22:17
up vote 3 down vote accepted

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. :) – J. M. Sep 26 '11 at 21:42
@J.M. Especially thoughts ... – Mark Bennet Sep 26 '11 at 22:01

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