文档介绍：ELEMENTARY
REAL ANALYSIS
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thomson·bruckner2
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Brian S. Thomson
Judith B. Bruckner
Andrew M. Bruckner
This PDF file is for the text Elementary Real Analysis originally pub-
lished by Prentice Hall (Pearson) in authors retain the copyright
and mercial uses.[2007]
Library of Congress Cataloging-in-Publication Data
Thomson, Brian S.
Elementary real analysis/ Brian S. Thomson,
Judith B. Bruckner, Andrew M. Bruckner.
p. cm.
Includes index.
ISBN:0-13-019075-6
1. Mathematical analysis. I. Bruckner, Judith B.
II. Bruckner, Andrew M. III. Title
QA300. T45 2001 00-041679
515–dc21 CIP
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ISBN: 0-13-019075-6
CONTENTS
PREFACE xii
1 PROPERTIES OF THE REAL NUMBERS 1
Introduction 1
The Real Number System 2
Algebraic Structure 5
Order Structure 8
Bounds 9
Sups and Infs 10
The Archimedean Property 13
Inductive Property of IN 15
The Rational Numbers Are Dense 16
The Metric Structure of R 18
Challenging Problems for Chapter 1 21
2 SEQUENCES 23
Introduction 23
Sequences 25
Sequence Examples 26