Why is 0! equal to 1?

How many ways can you arrange the elements in an empty set?

convenience

A factorial can be defined by the following formula :
n! = n × (n-1)!

Put n = 1 :
1! = 1 × 0!
1 = 1 × 0!

Then :
0! = 1

　
4!/4 = 3!
3!/3 = 2!
2!/2 = 1!
1!/1 = 0!

http://mathforum.org/library/drmath/view/57128.html

By the very fact that zzero '0' is a term number it is given a value of '1'

0! = 1