factorial

Consider the (trivial) fact that factorials can be calculated by recurrence:

n! = (n-1)! x n

Rearranging:

(n-1)! = n!/n

And setting n=1 we can deduce:

0! = (1-1)! = 1!/1 = 1/1 = 1

Also, it can be said that an empty set can only be ordered one way, so 0! = 1.