Maximum-minimums identity

Relates the maximum element of a set of numbers and the minima of its non-empty subsets 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 2n1 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 M. (2020). A First Course in Probability (Tenth, global ed.). Harlow, United Kingdom: Pearson. pp. 331–333. ISBN 978-1-292-26920-7.

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.