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Chapter 3 Sequences 3.1 Basic Properties Definition 3.1.1. A sequence is a function a : N ÷R. Instead of using the standard function notation of a(n) for sequences, it…

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Basic Analysis Introduction to Real Analysis by Jiˇ rí Lebl November 18, 2011 2 Typeset in L A T E X. Copyright c _2009–2011 Jiˇrí Lebl This work is licensed under…

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1. PMATH 351: Real Analysis Johnew Zhang July 30, 2013Contents 1 Axiom of Choice & Cardinality 1.1 Notation . . . . . . . . . . . . . . . . 1.2 Products & Axiom of…

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1. Lecture - 31Cauchy Sequences 2. Contents•Subsequences•Cauchy’s Convergence Criterion• CCC•Infinite Series2 3. SubSequence• Let (an) be a sequence. Let (nk)…

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1. Banach Contraction Mapping Principle Oksana Bihun March 2, 2010 Department of Mathematics and Computer Science Concordia College, Moorhead, MN 2. Stefan Banach Metric…

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Calculus for Cranks ©Nets Hawk Katz, 2014 Table of Contents Calculus for Cranks 1 1: Induction and the real numbers 1.1 Induction . . . . . . . . . . . . . . . . . . . .…

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Basic Analysis Introduction to Real Analysis with University of Pittsburgh supplements by Jirˇí Lebl August 3, 2012 2 Typeset in LATEX. Copyright c©2009–2011 Jirˇí…

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December 22, 2009 SMA 206: INTRODUCTION TO ANALYSIS Lecture Notes First Edition By Dr. Bernard Mutuku Nzimbi, PhD School of Mathematics, University of Nairobi P.o Box 30197,…

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One Variable Advanced Calculus Kenneth Kuttler October 11, 2013 2 Contents 1 Introduction 7 2 The Real And Complex Numbers 9 2.1 The Number Line And Algebra Of The Real Numbers…

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Introdu tion to Analysis Irena Swanson Reed College Spring 2014 Table of contents Preface 7 The briefest overview, motivation, notation 9 Chapter 1: How we will do mathematics…