Natural Number Addition is Associative

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 1
Follows directly from Natural Numbers under Addition is Commutative Monoid.

A monoid by definition is a semigroup.

Again by definition, the operation in a semigroup is associative.