Let ACR be a bounded non-empty set, and let B := {|x : x € A}. sup B-inf B≤ sup A - inf A (Hint: Find some [x] close to sup B and some ly close to inf B, then use the reverse triangle inequality.) Prove that

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...
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Let ACR be a bounded non-empty set, and let B := = {x| : x € A}.
sup B
inf B≤ sup A - inf A
(Hint: Find some |x| close to sup B and some ly close to inf B, then use the reverse triangle
inequality.)
Prove that
Transcribed Image Text:Let ACR be a bounded non-empty set, and let B := = {x| : x € A}. sup B inf B≤ sup A - inf A (Hint: Find some |x| close to sup B and some ly close to inf B, then use the reverse triangle inequality.) Prove that
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