The Integers and the Rational Numbers are Countable

Let $\mathbb{Z}$ be the set of integers and let $\mathbb{Q}$ be the set of rational numbers, both regarded as subsets of the real numbers. Then the following hold.

1. $\mathbb{Z}$ is countable.

2. $\mathbb{Q}$ is countable.

3. For every natural number $k$, the set $\mathbb{Q}^{k}$ of $k$-tuples in $\mathbb{Q}$ is countable.