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Prove each of the statements in two ways: (a) by contraposition and (b) by contradiction. The reciprocal of any irrational number is irrational. (The reciprocal of a nonzero real number y is 1/x.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.1: The Field Of Real Numbers

Problem 9TFE: Label each of the following statements as either true or false. Every decimal representation of a...

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Question

Prove each of the statements in two ways: (a) by contraposition and (b) by contradiction. The reciprocal of any irrational number is irrational. (The reciprocal of a nonzero real number y is 1/x.)

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