Finite Versus Infinite Contributions to an Eternal Dilemma
The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer
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Series Editors Douglas S. Bridges, Canterbury University, NZ Cristian S. Calude, University 0/Auckland, NZ Advisory Editorial Board J. Casti, Sante Fe Institute, USA G. J. Chaitin, IBM Research Center, USA E. W. Dijkstra, University o/Texas at Austin, USA J. Goguen, University o/California at San Diego, USA R. L. Graham, University 0/ California at San Diego, USA J. Hartmanis, Cornell University, USA H. Jurgensen, University o/Western Ontario, Canada A. Nerode, Cornell University, USA G. Rozenberg, Leiden University, The Netherlands A. Salomaa, Turku University, Finland
Cristian S. Calude and Gheorghe Paun
Finite Versus Infinite Contributions to an Eternal Dilemma
i
Springer
Cristian Calude Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand Gheorghe Paun Institute of Mathematics, Romanian Academy of Sciences, PO Box 1-764, 70700 Bucharest, Romania
ISBN-13:978-1-85233-251-8 e-ISBN-13: 978-1-4471-0751-4 DOl: 10.1007/978-1-4471-0751-4
Springer-Verlag Berlin Heidelberg New York British Library Cataloguing in Publication Data Finite versus infinite : contributions to an eternal Dilemma. - (Discrete mathematics and theoretical computer Science) 1. Infinite 2. Finite, The 3. Computer science - Mathematics 4. Mathematics - Philosophy 5. Mathematics - Data processing I. Calude, Christian S. II. Paun, Gheorghe 510 ISBN·13:978-1-85233-251-8 e-ISBN-J3:978-1-4471-0751-4 Library of Congress Cataloging-in-Publication Data Calude, Christian, 1952Finite versus infinite : contributions to an eternal dilemma 1 Christian S. Calude and Gheorghe Paun. p. cm. - (Discrete mathematics and theoretical computer science) Includes bibliographical references. ISBN-13:978-1-85233-251-8 e-ISBN-J3:978-1-4471-0751-4 1. Processes, Infinite. 2. Infinite. I. Paun, Gheorghe, 1950- II. Title. III. Series. QA295.C252000 515'.24-dc21 99-059492 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of repro graphic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. © Springer-Verlag London Limited 2000 Softcover reprint of the hardcover 1st edition 2000
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