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.
Other articles related to "rearrangement inequality":
... We will now prove by contradiction, that σ has to be the identity (then we are done) ... Assume that σ is not the identity ...
Famous quotes containing the word inequality:
“Love is a great thing. It is not by chance that in all times and practically among all cultured peoples love in the general sense and the love of a man for his wife are both called love. If love is often cruel or destructive, the reasons lie not in love itself, but in the inequality between people.”
—Anton Pavlovich Chekhov (18601904)