Definition:Factorial/Definition 1

Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.

The factorial of $n$ is defined inductively as:
 * $n! = \begin{cases}

1 & : n = 0 \\ n \paren {n - 1}! & : n > 0 \end{cases}$

Also see

 * Equivalence of Definitions of Factorial