The real numbers
To review our progress to date, we have rigorously constructed three fundamental number systems: the natural number system N, the integers Z, and the rationals Q 1. We defined the natural numbers using the five Peano axioms, and postulated that such a num
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Terence Tao
Analysis I Third Edition
Texts and Readings in Mathematics Volume 37
Advisory Editor C.S. Seshadri, Chennai Mathematical Institute, Chennai Managing Editor Rajendra Bhatia, Indian Statistical Institute, New Delhi Editor Manindra Agrawal, Indian Institute of Technology Kanpur, Kanpur V. Balaji, Chennai Mathematical Institute, Chennai R.B. Bapat, Indian Statistical Institute, New Delhi V.S. Borkar, Indian Institute of Technology Bombay, Mumbai T.R. Ramadas, Chennai Mathematical Institute, Chennai V. Srinivas, Tata Institute of Fundamental Research, Mumbai
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Terence Tao
Analysis I Third Edition
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Terence Tao Department of Mathematics University of California, Los Angeles Los Angeles, CA USA
This work is a co-publication with Hindustan Book Agency, New Delhi, licensed for sale in all countries in electronic form only. Sold and distributed in print across the world by Hindustan Book Agency, P-19 Green Park Extension, New Delhi 110016, India. ISBN: 978-93-80250-64-9 © Hindustan Book Agency 2015. ISSN 2366-8725 (electronic) Texts and Readings in Mathematics ISBN 978-981-10-1789-6 (eBook) DOI 10.1007/978-981-10-1789-6 Library of Congress Control Number: 2016940817 © Springer Science+Business Media Singapore 2016 and Hindustan Book Agency 2015 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
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