Definition:Factorial

Let $$n \in \mathbb{N}$$.

Then the factorial of $$n$$ is defined as:

$$ n! = \begin{cases} 1 : & n = 0 \\ \left({n - 1}\right)! \times n = \displaystyle\prod_{k=1}^n k: &\forall n > 0 \end{cases} $$

That is: $$n! = 1 \times 2 \times \cdots \times \left({n-1}\right) \times n$$.