Basic Set Theory
Seiten
2002
American Mathematical Society (Verlag)
978-0-8218-2731-4 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2731-4 (ISBN)
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Suitable for undergraduate students as well as professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma, this text introduces the main subjects of 'naive' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, and operations on ordinals.
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own dedicated treatment.This book provides just that in the form of a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ""naive"" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own dedicated treatment.This book provides just that in the form of a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ""naive"" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Sets and their cardinalities Ordered sets Bibliography Glossary Index.
| Erscheint lt. Verlag | 1.5.2006 |
|---|---|
| Reihe/Serie | Student Mathematical Library |
| Zusatzinfo | bibliography, index, glossary |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 164 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre |
| ISBN-10 | 0-8218-2731-6 / 0821827316 |
| ISBN-13 | 978-0-8218-2731-4 / 9780821827314 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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