Let $S\subseteq\mathbb{R}$. A number $\ell\in\mathbb{R}$ is called a lower bound of $S$ if $\ell\le s$ for every $s\in S$. If $S$ is nonempty and bounded below, then a number $m\in\mathbb{R}$ is called the greatest lower bound, or infimum, of $S$ if:

In that case one writes $m=\inf S$.