# Natural Numbers form Subsemiring of Integers

## Theorem

The semiring of natural numbers $\left({\N, +, \times}\right)$ forms a subsemiring of the ring of integers $\left({\Z, +, \times}\right)$.

## Proof

We have that Natural Numbers form Commutative Semiring.

From Natural Numbers are Non-Negative Integers we have that $\N$ is a subset of $\Z$.

Hence the result, from the definition of subsemiring.

$\blacksquare$