Let S be a set that is bounded below. Prove that a lower bound w of S

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Let S be a set that is bounded below. Prove that a lower bound w of S is the infimum of S if and only if for any ε > 0 there exists t ∈ S such that t < w + ε.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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