Minimum

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

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

Examples:

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