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Prove that between every two distinct real numbers there
Chapter 6, Problem 20E(choose chapter or problem)
Prove that between every two distinct real numbers there is a rational number (that is, a number of the form x/y, where x and y are integers with y ? 0).
Questions & Answers
QUESTION:
Prove that between every two distinct real numbers there is a rational number (that is, a number of the form x/y, where x and y are integers with y ? 0).
ANSWER:SolutionStep 1In this problem we need to prove that between every two distinct real numbers there is a rational number.That is to prove: a number of the form x/y, where x and y are integers with y 0.Let and be two distinct real numbers such that .We know that, “For every real number there exists an integer such that .” … (1)Here we have as a real number By (1), we getthere exists an integer such that … (2)