Contents PREFACE v Chapter 0 Preliminaries 0.1 SETS 2 0.2 RELATIONS AND FUNCTIONS 8 0.3 MATHEMATICAL INDUCTION AND RECURSION 12 0.4 EQUIVALENT AND COUNTABLE SETS 16 0.5 REAL NUMBERS 21 EXERCISES 27 PROJECTS 29 Chapter 1 Sequences 1.1 SEQUENCES AND CONVERGENCE 33 1.2 CAUCHY SEQUENCES 38 1.3 ARITHMETIC OPERATIONS ON SEQUENCES 42 1.4 SUBSEQUENCES AND MONOTONE SEQUENCES 49 EXERCISES 54 PROJECTS 57
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