Definition:Multiplication/Natural Numbers

Definition
The multiplication operation in the domain of natural numbers $\N$ is written $\times$.

It is defined as:


 * $\forall m, n \in \N: m \times n =

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

This can be interpreted as:


 * $n \times m = +^n m = \underbrace{m + m + \cdots + m}_{\text{$n$ copies of $m$}}$