Question

How can the factorial of 0 be 1?

Answer 1

If you know the value of `n!` then you can calculate `(n-1)!` as
`(n!)/n`; since `1! =1` then `0! = (1-1)! = 1/1 = 1`

Explanation:

Actually Nelson's answer if probably correct, but there is some justification for the definition.

Answer 2

Because there is one permutation of zero objects.

Explanation:

Interpreting `n!` to be the number of permutations of `n` objects.

And agreeing that there is a permutation of `0` object (namely the empty permutation).

Leads one to state that `0! = 1`

Answer 3

We can do some MATH and STUFF!

At `n_0 = 1`:
`(n!)/((n+1)!) = (1*cancel(2*3*4*...*n))/(cancel(2*3*4*5*...*n*)(n+1))`

`= 1/(n+1)`

If `(n!)/((n+1)!) = 1/(n+1) = (0!)/(1!)`, then, with `n = 0`:

`0! = 1!*(1/(0+1)) = (1!)/(1) = 1`