Maximum-minimums identity
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 nonempty subsets of S.
Let S = {x1, x2, ..., xn}. The identity
states that
or conversely
For a probabilistic proof, see the reference.
Let S = {x1, x2, ..., xn}. The identity
Identity (mathematics)
In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...
states that
or conversely
For a probabilistic proof, see the reference.