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Help with Real Analysis Problem

Exercise 2.6.6-Let AS Rbe a non - empty set, and let b e Rb e an upper bound of A. Suppose that for each e > 0, there is so E A such that b -e < a Prove that b lubA (In practice, it is often more convient to show that b-a 〈 ε, but we stated the exercise as we did to make it analogous to Lemma 2.6.5 (1) Lemma 2.6.5 (1) _ Let A, B R be non-empty sets, and let ε 〉 0. 1. Suppose that A has a least upper bound. Then there is some bEA such that lubA - E<a< lubA. 2.Suppose that A has a greatest lower bound. Then there is some b e A such that glbA S b < glbA + E

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