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Cover: 9780387900926 | Naive Set Theory | P. R. Halmos | Buch | HC runder Rücken kaschiert
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Naive Set Theory
Buch von P. R. Halmos
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Undergraduate Texts in Mathematics
Inhalt: vii
104 S.
1 s/w Illustr.
104 p. 1 illus.
ISBN-13: 9780387900926
ISBN-10: 0387900926
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Halmos, P. R.
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 13 mm
Von/Mit: P. R. Halmos
Erscheinungsdatum: 16.01.1998
Gewicht: 0,348 kg
Artikel-ID: 101267531
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Undergraduate Texts in Mathematics
Inhalt: vii
104 S.
1 s/w Illustr.
104 p. 1 illus.
ISBN-13: 9780387900926
ISBN-10: 0387900926
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Halmos, P. R.
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 13 mm
Von/Mit: P. R. Halmos
Erscheinungsdatum: 16.01.1998
Gewicht: 0,348 kg
Artikel-ID: 101267531
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