Maximum

A maximum of a subset $A\subseteq\mathbb R$ is an element $m\in A$ such that $x\le m$ for every $x\in A$.

If a maximum exists, it is unique and equals the supremum of $A$. Many sets have a supremum but no maximum (for instance, open intervals).

Examples:

• For $A=[0,1]$, the maximum is $1$.
• For $A=\{2,5,3\}$, the maximum is $5$.