2000 Mathematics Subject Classification. Primar y 26-01. For additional information and updates on this book, visit w w w . a m s . o r g / b o o k p a g e s / a m s t e x t - l Librar y of Congres s Cataloging-in-Publication Dat a Gaughan, Edward. Introduction to analysis—5th ed. / Edward D. Gaughan. p. cm. (Pure and applied undergraduate texts v. 1) Includes index. ISBN 978-0-8218-4787-9 (alk. paper) 1. Mathematical analysis. I. Title. QA300.G34 2009 515—-dc22 2008047387 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permission9ams.org. © 1968, 1975, 1987, 1993, 1998 held by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at h t t p : //www. ams. org/ 10 9 8 7 6 5 4 3 2 14 13 12 11 10 09
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