Maximum-minimums identity

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https://en.wikipedia.org/wiki/Maximum-minimums_identity

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 2n − 1 non-empty subsets of S.

Let S = {x1, x2, ..., xn}. The identity states that

or conversely

For a probabilistic proof, see the reference.

See also

References

  • Ross, Sheldon (2002). A First Course in Probability. Englewood Cliffs: Prentice Hall. ISBN  0-13-033851-6.