The infinite set of real numbers R is not denumerable (that is, N O < IRI). it
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The infinite set of real numbers R is not denumerable (that is, NO < IRI). it suffices to show that the open interval (0,1) You may assume each real number can be written as an infinite decimal. If (0, 1) is denumerable there is a bijection f: N* → (0, 1 ). Construct an infinite decimal (real number) .a1a2· · · in {0,1) such that an is not the nth digit in the decimal expansion of f(n). This number cannot be in Im f.]
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To prove that the open interval 01 is not denumerable we will use a proof by contradiction Assume th...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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