Natural Number Addition is Commutative/Proof 1

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


 * $\forall x, y \in \N: x + y = y + x$

Proof
We have that the Natural Numbers are a Naturally Ordered Semigroup whose operation is addition.

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

Hence the result.