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Let S be a non-empty bounded subset of R and let a be an upper bound of S. Show hat sup S = a if and only for any positve real number e, there is s E S, with a-€ < s.

Let S be a non-empty bounded subset of R and let a be an upper bound of S. Show hat sup S = a if and only for any positve real number e, there is s E S, with a-€ < s.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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3. Let S be a non-empty bounded subset of R and let a be an upper bound of S. Show that sup S = a if and only for any positve real number e, there is s E S, with a-e < s.
Transcribed Image Text:3. Let S be a non-empty bounded subset of R and let a be an upper bound of S. Show that sup S = a if and only for any positve real number e, there is s E S, with a-e < s.
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