Natural Number Addition is Associative/Proof 1

Theorem

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

$\forall x, y, z \in \N: x + \paren {y + z} = \paren {x + y} + z$

Proof

Consider the natural numbers defined as a naturally ordered semigroup.

By definition, the operation in a semigroup is associative.

Hence the result.

$\blacksquare$