Natural Numbers form Subsemiring of Integers

Theorem

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

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.

$\blacksquare$