Let (an) be an increasing sequence, (bn) be a decreasing sequence, and assume that an < bn

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Let (an) be an increasing sequence, (bn) be a decreasing sequence, and assume that an < bn for all n ∈ N. Show that lim(an) < lim(bn), and thereby deduce the Nested Intervals Property 2.5.2 from the Monotone Convergence Theorem 3.3.2.

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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 10:55 AM

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Let (an) be an increasing sequence, (bn) be a decreasing sequence, and assume that an < bn

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The sequence an is increasing and is bounded ...View the full answer

Introduction to Real Analysis

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