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a Let r Q (0, 1). Write r = where a 21 and b 21 are coprime natural numbers. Show that there exists a natural number n ≥ 1 such that b a 1 n+ Use this to show that there exist natural numbers n₁,...,nk such that a 1 T= - +... + n1 . nk

a Let r Q (0, 1). Write r = where a 21 and b 21 are coprime natural numbers. Show that there exists a natural number n ≥ 1 such that b a 1 n+ Use this to show that there exist natural numbers n₁,...,nk such that a 1 T= - +... + n1 . nk

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 13E: 13. Let Z denote the set of all integers, and let Prove that .
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Let re Qn (0, 1). Write r where a 1 and b≥ 1 are coprime natural numbers. Show that there exists a natural number n ≥ 1 such that 1 a 1 n+ Use this to show that there exist natural numbers n₁,...,nk such that + +== nk
Transcribed Image Text:Let re Qn (0, 1). Write r where a 1 and b≥ 1 are coprime natural numbers. Show that there exists a natural number n ≥ 1 such that 1 a 1 n+ Use this to show that there exist natural numbers n₁,...,nk such that + +== nk
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