Introduction to Abstract Mathematics

Preface

Acknowledgments

I. Logic and Set Theory

1.1 Introduction

1.2 Statements and Open Sentences

Exercises 1.2

1.3 Sets

Exercises 1.3

1.4 Ordered Pairs and Relations

Exercises 1.4

1.5 Functions and Kindred Matters

Exercises 1.5

1.6 Axiom Systems and Methods of Proof

II. The Natural Numbers

2.1 Introduction

2.2 Arithmetic

Exercises 2.2

2.3 Ordering

Exercises 2.3

III. The Integers and the Rational Numbers

3.1 Introduction

3.2 Preliminaries

Exercises 3.2

3.3 Additional Topics

Exercises 3.3

3.4 The Rational Numbers and Ordered Fields

Exercises 3.4

IV. The Real and Complex Numbers

4.1 Introduction

4.2 Construction of R

Exercises 4.2

V. Metric Spaces

5.1 Introduction

5.2 Definition and Basic Properties

Exercises 5.2

5.3 Openness, Closedness, and Neighborhood Systems

Exercises 5.3

5.4 Continuous Functions

Exercises 5.4

VI. Limits

6.1 Introduction

Exercise 6.1

6.2 Generalized Limits

Exercises 6.2

6.3 Some Examples

Exercises 6.3

References

Answers to Selected Exercises

Subject Index