Problem on rearrangement inequality I read that the rearrangement inequality deals with sorted sequences of real numbers. We have $-5>-6$ and $3>2$ , hence by rearrangement inequality we have $-15>-12$ which is obviously false.
What am I missing out?

In this context the rearrangement inequality says that 
$$
x_1 = -6 < -5 = x_2 \text{ and } y_1 = 2 < 3 = y_2
$$
implies that 
$$
-28 = -18 -10 = x_1 y_2 + x_2 y_1  \le  x_1 y_1 + x_2 y_2 = -12 -15 =-27,
$$
which is true.  It does not say what you're asserting.
