Prove that the set of irrational numbers in [0,1] is not countable.

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 18E: Prove that if is an irrational number, then is an irrational number.
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Prove that the set of irrational numbers in [0,1] is not countable.

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