Integers form Subdomain of Rationals

Theorem

The integral domain of integers $\left({\Z, +, \times}\right)$ forms a subdomain of the field of rational numbers.

Proof

The rational numbers are defined as the quotient field of the integers.

From its method of construction, it follows that the integers $\Z$ are a subset of the rational numbers $\Q$.

Hence the result, from the definition of subdomain.

$\blacksquare$