Definition:Multiplication/Natural Numbers/Addition

Definition
Let $\N$ be the natural numbers. Let $+$ denote addition.

The binary operation $\times$ is defined on $\N$ as follows:
 * $\forall m, n \in \N: \begin{cases}

m \times 0 & = 0 \\ m \times \left({n + 1}\right) & = m \times n + m \end{cases}$

This operation is called multiplication.

The definition can equivalently be structured:
 * $\forall m, n \in \N: \begin{cases}

0 \times n & = 0 \\ \left({m + 1}\right) \times n & = n + m \times n \end{cases}$