Problem #PRU-109685

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Linear inequalites and systems of inequalities Methods Proof by contradiction Calculus Real numbers Rational and irrational numbers
 14–16  4.0

Problem

At all rational points of the real line, integers are arranged. Prove that there is a segment such that the sum of the numbers at its ends does not exceed twice the number on its middle.