Minimum

definitionreal-analysis

Definition

If $m$ is a lower bound of a subset $S\subset \mathbb{R}$, and $m\in S$, we call $m$ the (unique) minimum of $S$.

Lower Bound

For a subset $S\subset \mathbb{R}$, if $a$ is a real number such that for all $x\in S$, $a\le x$, we say that $a$ is a lower bound of $S$.

Examples