# Natural Numbers under Addition form Commutative Semigroup

## Theorem

The algebraic structure $\left({\N, +}\right)$ consisting of the set of natural numbers $\N$ under addition $+$ is a commutative semigroup.

## Proof

Consider the natural numbers $\N$ defined as the naturally ordered semigroup.

From the definition of the naturally ordered semigroup, it follows that $\left ({\N, +}\right)$ is a commutative semigroup.

$\blacksquare$