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Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number mEN such that m

Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number mEN such that m

Elements Of Modern Algebra
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 each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m<a<m+1 (b) Prove that 2" <m! + 2 for m € N. (c) For any nonzero real number z, prove Σ1-1
Transcribed Image Text:Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m<a<m+1 (b) Prove that 2" <m! + 2 for m € N. (c) For any nonzero real number z, prove Σ1-1
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Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m<a<m+1 (b) Prove that 2" <m! + 2 for m € N. (c) For any nonzero real number z, prove Σ1-1
Transcribed Image Text:Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural number m € N such that m<a<m+1 (b) Prove that 2" <m! + 2 for m € N. (c) For any nonzero real number z, prove Σ1-1
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