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Unformatted text preview: The Zakon Series on Mathematical Analysis Basic Concepts of Mathematics Mathematical Analysis I Mathematical Analysis II 9 781931 705028 The Zakon Series on Mathematical Analysis Mathematical Analysis Volume I Elias Zakon University of Windsor The Trillia Group West Lafayette, IN Terms and Conditions You may download, print, transfer, or copy this work, either electronically or mechanically, only under the following conditions. If you are a student using this work for selfstudy, no payment is required. If you are a teacher evaluating this work for use as a required or recommended text in a course, no payment is required. Payment is required for any and all other uses of this work . In particular, but not exclusively, payment is required if (1) you are a student and this is a required or recommended text for a course; (2) you are a teacher and you are using this book as a reference, or as a required or recommended text, for a course. Payment is made through the website http://www.trillia.com . For each individual using this book, payment of US$10 is required. A sitewide payment of US$300 allows the use of this book in perpetuity by all teachers, students, or employees of a single school or company at all sites that can be contained in a circle centered at the location of payment with a radius of 25 miles (40 kilometers). You may post this work to your own website or other server (FTP, etc.) only if a sitewide payment has been made and it is noted on your website (or other server) precisely which people have the right to download this work according to these terms and conditions. Any copy you make of this work, by any means, in whole or in part, must contain this page, verbatim and in its entirety. Mathematical Analysis I c circlecopyrt 1975 Elias Zakon c circlecopyrt 2004 Bradley J. Lucier and Tamara Zakon ISBN 978193170502X Published by The Trillia Group, West Lafayette, Indiana, USA First published: May 20, 2004. This version released: May 24, 2010. Technical Typist: Betty Gick. Copy Editor: John Spiegelman. Logo: Miriam Bogdanic. The phrase The Trillia Group and The Trillia Group logo are trademarks of The Trillia Group. This book was prepared by Bradley J. Lucier and Tamara Zakon from a manuscript written by Elias Zakon. We intend to correct and update this work as needed. If you notice any mistakes in this work, please send email to lucier@math.purdue.edu and they will be corrected in a later version. Contents Preface ix About the Author xi Chapter 1. Set Theory 1 13. Sets and Operations on Sets. Quantifiers ........................... 1 Problems in Set Theory ......................................... 6 47. Relations. Mappings ............................................... 8 Problems on Relations and Mappings ........................... 14 8. Sequences ........................................................ 15 9. Some Theorems on Countable Sets ................................ 18 Problems on Countable and Uncountable Sets...
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