Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Enclosed binary operation
Groupoid
Semigroup
Monoid
Multiplicative monoid of integers
Multiplicative monoid of natural numbers
Natural number factorial function
Basic natural number factorial
Formulation 0
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}
Formulation 1
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}