In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2<sup>n</sup> âÂÂ 1 non-empty subsets of S.
Let S = {x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>}. The identity states that
or conversely
For a probabilistic proof, see the reference.