Contents
Preface vii
Chapter 1. The Real Numbers 1
1.1. Sets and Functions 2
1.2. The Natural Numbers 8
1.3. Integers and Rational Numbers 16
1.4. The Real Numbers 21
1.5. Sup and Inf 26
Chapter 2. Sequences 33
2.1. Limits of Sequences 33
2.2. Using the Definition of Limit 38
2.3. Limit Theorems 42
2.4. Monotone Sequences 46
2.5. Cauchy Sequences 51
2.6. lim inf and lim sup 55
Chapter 3. Continuous Functions 59
3.1. Continuity 59
3.2. Properties of Continuous Functions 65
3.3. Uniform Continuity 69
3.4. Uniform Convergence 73
Chapter 4. The Derivative 79
4.1. Limits of Functions 79
4.2. The Derivative 84
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