Knowlpedia

Maximum

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

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

Remarks

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

Examples
  • For A=[0,1]A=[0,1], the maximum is 11.
  • For A={2,5,3}A=\{2,5,3\}, the maximum is 55.