Natural Numbers under Multiplication form Semigroup

Theorem
Let $\N$ be the set of natural numbers.

Let $\times$ denote the operation of multiplication on $\N$.

The structure $\left({\N, \times}\right)$ forms a semigroup.

Closure
We have that Natural Number Multiplication is Closed.

That is, $\left({\N, \times}\right)$ is closed.

Associativity
We have that Natural Number Multiplication is Associative.

Thus the criteria are fulfilled for $\left({\N, \times}\right)$ to form a semigroup.