Why is 0 factorial 1,1 factorial 1,2 factorial 2?

Why is 0 factorial 1,1 factorial 1,2 factorial 2?

The factorial of 1 is 1 = 1
The factorial of 2 is 2 * 1 = 2
The factorial of 0 is a special case equal to 1
The factorial of n is n * (n-1) *... * 1