Let $N \in \mathbb{N}$ be a D996: Natural number.
The factorial of $N$ is the D996: Natural number $$\begin{equation} N ! : = \begin{cases} \prod_{n = 1}^N n, \quad & N > 0 \\ 1, \quad & N = 0 \end{cases} \end{equation}$$

Let $N \in \mathbb{N}$ be a D996: Natural number.
The factorial of $N$ is the D996: Natural number $$\begin{equation} N ! : = I_{N > 0} \left( \prod_{n = 1}^N n \right) + I_{N = 0} \end{equation}$$