Natural Number Addition is Associative/Proof 1

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


 * $\forall x, y, z \in \N: x + \left({y + z}\right) = \left({x + y}\right) + z$

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

By definition, the operation in a semigroup is associative.

Hence the result.