Let $S \subseteq \mathbb{R}$ be nonempty and bounded below. A number $t$ is the \emph{infimum} of $S$ if: (i) $t$ is a lower bound of $S$; and (ii) for every $\varepsilon>0$ there exists $x\in S$ with $x < t+\varepsilon$. We write $t=\inf S$.