Archimedean property of R

Archimedean property of $\mathbb{R}$: For every $x\in\mathbb{R}$ there exists $n\in\mathbb{N}$ such that $n>x$. Equivalently, for every $\varepsilon>0$ there exists $n\in\mathbb{N}$ such that $1/n<\varepsilon$.

This property links the discrete structure of $\mathbb{N}$ to the continuum $\mathbb{R}$ and is used constantly in $\varepsilon$–$N$ arguments, especially to choose large integers making quantities small.