\begin{definition}[Definition:Factorial/Definition 2]
Let $n \in \Z_{\ge 0}$ be a positive integer.
The '''factorial of $n$''' is defined as:
{{begin-eqn}}
{{eqn | l = n!
      | r = \prod_{k \mathop = 1}^n k
      | c = 
}}
{{eqn | r = 1 \times 2 \times \cdots \times \paren {n - 1} \times n
      | c = 
}}
{{end-eqn}}
where $\ds \prod$ denotes product notation.
\end{definition}