Expert: Steve Holleran - 10/26/2007

Question
Hi Mr.Steve,
I am confused by the following two statements.
0!=1
1!=1
Is there any proofs to the above facts?
Thanks.

Answer
Hi Hassan,

Well, these are definitions, not theorems, so they require no proof.  since n! means 1 * 2 * ... * n, it would follow that 1! = 1.  

Having 0! = 1 is helpful in counting problems.  For example, to order n objects, the number of ways is n!.  For example, if I try to seat 3 students in a row, there are 3! = 6 ways to do this.  Well, if I want to order 0 students, there is only 1 way to do this: to not order them, so it helps that 0! = 1.

Steve