Natural Number Addition is Commutative/Proof 1

Theorem

The operation of addition on the set of natural numbers $\N$ is commutative:

$\forall m, n \in \N: m + n = n + m$

Proof

Consider the natural numbers defined as a naturally ordered semigroup.

By definition, the operation in a naturally ordered semigroup is commutative.

Hence the result.

$\blacksquare$