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Let I R be an interval and let f : I R be increasing on I. Suppose that

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Let I ⊂ R be an interval and let f : I → R be increasing on I. Suppose that c ∈ I is not an endpoint of I. Show that f is continuous at c if and only if there exists a sequence (xn) in I such that xn < c for n = 1, 3, 5, . . . ; xn > c for n = 2, 4, 6, . . . ; and such that c = lim(xn) and f(c) = lim (f(xn)).

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Introduction to Real Analysis

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: April 07, 2016 11:02:36
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