Jump to content

Maximum-minimums identity

From Wikipedia, the free encyclopedia

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

[edit]

References

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