1549901369-Elements_of_Real_Analysis__Denlinger_

Contents

Preface

To the Student

To the Instructor

1

2

3

The Real Number System

1.1 The Field Properties

1.2 The Order Properties

1.3 Natural Numbers ..

1.4 Rational Numbers..

1.

1.

1.

The Archimedean Property.

The Completeness Property

*"The" Complete Ordered Field

Sequences

2.1 B asic Concepts: Convergence and Limits

2.2 Algebra of Limits ...

2.3 Inequalities and Limits

2.4 Divergence to Infinity.

2.5 Monotone Sequences.

2.6 Subsequences and Cluster Points.

2.

2.

2.

Cauchy Sequences.........

*countable and Uncountable Sets

*Upper and Lower Limits

Topology of the Real Number System

3.1 Neighborhoods and Open Sets.

3.2 Closed Sets and Cluster Points.

3.3 * Compact Sets.....

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