Mathematical Structures
In this chapter we study some of the main structures that form the building blocks of mathematics. As a way of introduction, we revisit a point we made earlier about statements and sets.
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Béla Bajnok
An Invitation to Abstract Mathematics Second Edition
Undergraduate Texts in Mathematics
Undergraduate Texts in Mathematics
Series Editors Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA
Advisory Board Colin Adams, Williams College, Williamstown, MA, USA L. Craig Evans, University of California, Berkeley, CA, USA Pamela Gorkin, Bucknell University, Lewisburg, PA, USA Roger E. Howe, Yale University, New Haven, CT, USA Michael E. Orrison, Harvey Mudd College, Claremont, CA, USA Lisette G. de Pillis, Harvey Mudd College, Claremont, CA, USA Jill Pipher, Brown University, Providence, RI, USA Jessica Sidman, Mount Holyoke College, South Hadley, MA, USA
Undergraduate Texts in Mathematics are generally aimed at third- and fourthyear undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interrelations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding.
More information about this series at http://www.springer.com/series/666
Béla Bajnok
An Invitation to Abstract Mathematics Second Edition
Béla Bajnok Department of Mathematics Gettysburg College Gettysburg, PA, USA
ISSN 0172-6056 ISSN 2197-5604 (electronic) Undergraduate Texts in Mathematics ISBN 978-3-030-56173-4 ISBN 978-3-030-56174-1 (eBook) https://doi.org/10.1007/978-3-030-56174-1 Mathematics Subject Classification: 00, 01, 03 1st edition: © Béla Bajnok 2013 2nd edition: © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, 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 publisher, 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 publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerlan
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