an introduction to mathematical reasoning

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 1/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 2/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 3/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 4/69

c

and to the provisions of relevant collective licensing agreements,

no reproduction of any part may take place withoutthe written permission of Cambridge University Press.

Printed in the United Kingdom at the University Press, Cambridge

Library of Congress Cataloging in Publication data

p. cm.

1. I. Title.

CIP

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sa~o Paulo

Cambridge University Press

This publication is in copyright. Subject to statutory exception

Cambridge UniversityPress has no responsibility for the persistence or accuracy

accurate or appropriate.

Information on this title:www.cambridge.org/9780521597180

Cambridge University Press 2007

First published 1997

 A catalogue record of this publication is available from the British Library

Eccles, Peter J., 1945-An introduction to mathematical reasoning: lectures on numbers, sets,

and functions / Peter J. Eccles.

Includes bibliographical references and index.ISBN 0 521 59269 0 hardback -- ISBN 0 521 59718 8 paperback

Proof theory.QA9.54.E23 1997

511.3–dc21 97-11977

The Edinburgh Building, Cambridge, CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

ISBN 978-0-521-59718-0 paperback

Tenth printing 2007

CAMBRIDGE UNIVERSITY PRESS

and does not guaranteethat any content on such websites is, or will remain,of URLs for external or third-party intenet websites referred to in thispublication,

ISBN 978-0-521-59269-7 hardback

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 5/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 6/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 7/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 8/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 9/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 10/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 11/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 12/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 13/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 14/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 15/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 16/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 17/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 18/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 19/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 20/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 21/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 22/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 23/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 24/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 25/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 26/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 27/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 28/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 29/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 30/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 31/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 32/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 33/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 34/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 35/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 36/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 37/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 38/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 39/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 40/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 41/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 42/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 43/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 44/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 45/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 46/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 47/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 48/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 49/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 50/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 51/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 52/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 53/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 54/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 55/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 56/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 57/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 58/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 59/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 60/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 61/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 62/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 63/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 64/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 65/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 66/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 67/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 68/69

7/28/2019 An Introduction to Mathematical Reasoning

http://slidepdf.com/reader/full/an-introduction-to-mathematical-reasoning 69/69