# Integers form Subring of Reals

## Theorem

The ring of integers $\struct {\Z, +, \times}$ forms a subring of the field of real numbers.

## Proof

We have that the set of integers $\Z$ are a subset of the real numbers $\R$.

The field of real numbers is, a fortiori, also a ring.

Hence the result, by definition of subring.

$\blacksquare$