In mathematics, the rearrangement inequality states that
for every choice of real numbers
and every permutation
of x1, . . ., xn. If the numbers are different, meaning that
then the lower bound is attained only for the permutation which reverses the order, i.e. σ(i) = n − i + 1 for all i = 1, ..., n, and the upper bound is attained only for the identity, i.e. σ(i) = i for all i = 1, ..., n.
Note that the rearrangement inequality makes no assumptions on the signs of the real numbers.
Read more about Rearrangement Inequality: Applications, Proof
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