Knowlpedia

Minimum

The smallest element of a set of real numbers, when it exists.

A minimum of a A⊆RA\subseteq\mathbb R is an element m∈Am\in A such that m≤xm\le x for every x∈Ax\in A.

Remarks

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

Examples
  • For A=[0,1]A=[0,1], the minimum is 00.
  • For A={2,5,3}A=\{2,5,3\}, the minimum is 22.