Maximum

definitionreal-analysis

Definition

If $M$ is an upper bound of a subset $S\subset \mathbb{R}$, and $M\in S$, we call $M$ the (unique) maximum of $S$.

Upper Bound

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

Examples