Classical inequalities (other)

Besides the most famous inequalities like AM-GM and Cauchy-Schwarz, there are several other classical inequalities that are useful in olympiad problem solving. These include the rearrangement inequality, Chebyshev's inequality, Nesbitt's inequality, and others. Each provides a way to compare sums or products of numbers under certain conditions.

Important properties

• The rearrangement inequality states that arranging numbers in the same order maximizes the sum of their products.

• Chebyshev's inequality relates the sum of products of similarly ordered sequences.

• Nesbitt's inequality gives a lower bound for a specific cyclic sum involving three positive numbers.

• These inequalities often require the numbers involved to be ordered or positive.