Let ACBCR, and assume that B is bounded. i) Prove that A is bounded ii) Prove...

 

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Let ACBCR, and assume that B is bounded. i) Prove that A is bounded ii) Prove rigorously that inf(B) ≤ inf(A) ≤ sup(A) ≤ sup(B). Extrelse 5. Find sets A, B CR such that x < y for all x EA and y E B, and yet sup(A) = inf(B). Let ACBCR, and assume that B is bounded. i) Prove that A is bounded ii) Prove rigorously that inf(B) ≤ inf(A) ≤ sup(A) ≤ sup(B). Extrelse 5. Find sets A, B CR such that x < y for all x EA and y E B, and yet sup(A) = inf(B).

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i To prove that A is bounded we need to show that there exists a real number M 0 such that a M for a... View the full answer