Use the Heine-Borel Theorem to prove the following version of the Bolzano-Weierstrass Theorem: Every bounded infinite subset

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Use the Heine-Borel Theorem to prove the following version of the Bolzano-Weierstrass Theorem: Every bounded infinite subset of R has a cluster point in R. (If a set has no cluster points, then it is closed by Theorem 11.1.8.)

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 11:13 AM

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Use the Heine-Borel Theorem to prove the following version of the Bolzano-Weierstrass Theorem: Every bounded infinite subset

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Let K be a bounded infinite subset of R we want to show t...View the full answer

Introduction to Real Analysis

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