Notes on Set Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | What this book is about. The theory of sets is a vibrant, exciting mathematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foundation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "abstract sets," including the Axiom of Choice, transfinite recursion, and cardinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning |
| Beschreibung: | 1 Online-Ressource (XIV, 273 p) |
| ISBN: | 9781475741537 9781475741551 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4757-4153-7 |
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Datensatz im Suchindex
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| author_facet | Moschovakis, Yiannis N. |
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| author_sort | Moschovakis, Yiannis N. |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4153-7 |
| format | Electronic eBook |
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| id | DE-604.BV042421583 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475741537 9781475741551 |
| issn | 0172-6056 |
| language | English |
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| physical | 1 Online-Ressource (XIV, 273 p) |
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| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Springer New York |
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| series2 | Undergraduate Texts in Mathematics |
| spelling | Moschovakis, Yiannis N. Verfasser aut Notes on Set Theory by Yiannis N. Moschovakis New York, NY Springer New York 1994 1 Online-Ressource (XIV, 273 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 What this book is about. The theory of sets is a vibrant, exciting mathematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foundation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "abstract sets," including the Axiom of Choice, transfinite recursion, and cardinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-4153-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moschovakis, Yiannis N. Notes on Set Theory Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Notes on Set Theory |
| title_auth | Notes on Set Theory |
| title_exact_search | Notes on Set Theory |
| title_full | Notes on Set Theory by Yiannis N. Moschovakis |
| title_fullStr | Notes on Set Theory by Yiannis N. Moschovakis |
| title_full_unstemmed | Notes on Set Theory by Yiannis N. Moschovakis |
| title_short | Notes on Set Theory |
| title_sort | notes on set theory |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Mengenlehre |
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