In mathematics, the **rearrangement inequality** states that

for every choice of real numbers

and every permutation

of *x*_{1}, . . ., *x _{n}*. 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

### Other articles related to "rearrangement inequality":

**Rearrangement Inequality**- Proof

... We will now prove by contradiction, that σ has to be the identity (then we are done) ... Assume that σ is not the identity ...

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