Understanding Real Analysis

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Front Cover; Copyright ; Table of Contents; Preface; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Solutions.Preface 1 Preliminaries: Numbers, Sets, Proofs, and BoundsNumbers 101: The Very BasicsSets 101: Getting StartedSets 102: The Idea of a FunctionProofs 101: Proofs and Proof-WritingTypes of ProofSets 103: Finite and Infinite Sets; CardinalityNumbers 102: Absolute ValuesBoundsNumbers 103: Completeness2 Sequences and Series SequencesandConvergenceWorkingwithSequencesSubsequencesCauchySequencesSeries 101: Basic IdeasSeries 102: Testing for Convergence and Estimating LimitsLimsupandliminf:AGuidedDiscovery3 Limits and Continuity LimitsofFunctionsContinuous FunctionsWhyContinuityMatters:ValueTheoremsU. Read more... Abstract: Front Cover; Copyright ; Table of Contents; Preface; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Solutions.Preface 1 Preliminaries: Numbers, Sets, Proofs, and BoundsNumbers 101: The Very BasicsSets 101: Getting StartedSets 102: The Idea of a FunctionProofs 101: Proofs and Proof-WritingTypes of ProofSets 103: Finite and Infinite Sets; CardinalityNumbers 102: Absolute ValuesBoundsNumbers 103: Completeness2 Sequences and Series SequencesandConvergenceWorkingwithSequencesSubsequencesCauchySequencesSeries 101: Basic IdeasSeries 102: Testing for Convergence and Estimating LimitsLimsupandliminf:AGuidedDiscovery3 Limits and Continuity LimitsofFunctionsContinuous FunctionsWhyContinuityMatters:ValueTheoremsU