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 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 M. (2020). A First Course in Probability (Tenth, global ed.). Harlow, United Kingdom: Pearson. pp. 331–333. ISBN 978-1-292-26920-7.
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