 Chebyshev's sum inequality

Chebyshev's sum inequality is a fundamental result in the field of mathematics, particularly in inequalities and statistics. It illustrates the relationship between the sums of ordered sequences of variables. The inequality can be stated as follows: Let \( (a_1, a_2, \ldots, a_n) \) and \( (b_1, b_2, \ldots, b_n) \) be two sequences of real numbers.