Factorial/Examples/0

Example of Factorial
The factorial of $0$ is $1$:
 * $0! = 1$

Proof
From the definition of factorial:
 * $n! = \displaystyle \prod_{k \mathop = 1}^n k$

where $\prod$ denotes product notation.

When $n = 0$ we have:
 * $0! = \displaystyle \prod_{k \mathop = 1}^0 k$

Hence the result, by definition of vacuous product.