3. Let S R be a non-empty set which is bounded above. Prove that for every e > 0 there is an element z ES such that (sup S) - € < x≤ sup S.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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3. Let S CR be a non-empty set which is bounded above. Prove that for every € > 0
there is an element r ES such that (sup S) - €< x < sup S.
T lilin|
Transcribed Image Text:3. Let S CR be a non-empty set which is bounded above. Prove that for every € > 0 there is an element r ES such that (sup S) - €< x < sup S. T lilin|
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