Let $\theta \in \mathbb{R}$ and let $N \in \mathbb{N}$. There exist integers $p \in \mathbb{Z}$ and $q \in \mathbb{N}$ with $1 \leq q \leq N$ such that
Consequently, if $\theta$ is irrational, then there exist infinitely many distinct rational numbers $p/q$, with $p \in \mathbb{Z}$ and $q \in \mathbb{N}$, such that