Naive set theory
by Halmos, Paul R., (Paul Richard)
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or m…
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- Full title :Naive set theory / by Paul R. Halmos.
Summary
Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.
Read More ↓Edition Statements
- Publication Date:1974
Publication Statements
- Publisher(s):Springer-Verlag
- Place of Publication:New York
- Language:eng
- Publication Date:1974
Notes
Reprint of the 1960 ed. published by Van Nostrand, Princeton, N.J., in series: The University series in undergraduate mathematics.
The Physical Object
- Description:1 online resource (vii, 104 pages)
Edition Identifiers
- ISBN:9781475716450, 1475716451, 9780387901046, 0387901043
- DOI:10.1007/978-1-4757-1645-0
- oclc:ocn883391473
- LC Classification:QA248
- Dewey Decimal:511/.3
Table of Contents
1. The axiom of extension -- 2. The axiom of specification -- 3. Unordered pairs -- 4. Unions and intersections -- 5. Complements and powers -- 6. Ordered pairs -- 7. Relations -- 8. Functions -- 9. Families -- 10. Inverses and composites -- 11. Numbers -- 12. The Peano axioms -- 13. Arithmetic -- 14. Order -- 15. The axiom of choice -- 16. Zorn's Lemma -- 17. Well ordering -- 18. Transfinite recursion -- 19. Ordinal numbers -- 20. Sets of ordinal numbers -- 21. Ordinal arithmetic -- 22. The Schröder-Bernstein theorem -- 23. Countable sets -- 24. Cardinal arithmetic -- 25. Cardinal numbers.
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