Suppose that E R is a nonempty bounded set and that sup E E. Prove

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Suppose that E ⊂ R is a nonempty bounded set and that sup E ∉ E. Prove that there exists a strictly increasing sequence {xn} that converges to sup E such that xn ∊ E for all n ∊ N.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:55 AM

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Suppose that E R is a nonempty bounded set and that sup E E. Prove

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Choose by the Approximation Property a n x 1 E such that supE 1 x 1 supE Since s...View the full answer

An Introduction to Analysis

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