Natural Numbers under Addition form Commutative Semigroup
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Theorem
The algebraic structure $\struct {\N, +}$ 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 $\struct {\N, +}$ is a commutative semigroup.
$\blacksquare$