Question

The quantity 0! is defined equal to 1. Tell why this definition is reasonable.

Answer 1

The common notion is that, since n!/n = (n-1)!, we can substitute 1 in for n and we can see that 0! is 1. The problem with this is that, if 0! is not assumed to be 1 (which is an assumption mathematicians do make), this rule will only hold for values of n that are equal to or greater than 2. To see why, let's look at the proof that n!/n = (n-1)!: