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Beschreibung
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Inhaltsverzeichnis
1. INTRODUCTION
1.1 Set Theory and the Foundations of Mathematics
1.2 Logic and Notation
1.3 Axiom Schema of Abstraction and Russell's Paradox
1.4 More Paradoxes
1.5 Preview of Axioms
2. GENERAL DEVELOPMENTS
2.1 Preliminaries: Formulas and Definitions
2.2 Axioms of Extensionality and Separation
2.3 "Intersection, Union, and Difference of Sets "
2.4 Pairing Axiom and Ordered Pairs
2.5 Definition by Abstraction
2.6 Sum Axiom and Families of Sets
2.7 Power Set Axiom
2.8 Cartesian Product of Sets
2.9 Axiom of Regularity
2.10 Summary of Axioms
3. RELATIONS AND FUNCTIONS
3.1 Operations on Binary Relations
3.2 Ordering Relations
3.3 Equivalence Relations and Partitions
3.4 Functions
4. "EQUIPOLLENCE, FINITE SETS, AND CARDINAL NUMBERS "
4.1 Equipollence
4.2 Finite Sets
4.3 Cardinal Numbers
4.4 Finite Cardinals
5. FINITE ORDINALS AND DENUMERABLE SETS
5.1 Definition and General Properties of Ordinals
5.2 Finite Ordinals and Recursive Definitions
5.3 Denumerable Sets
6. RATIONAL NUMBERS AND REAL NUMBERS
6.1 Introduction
6.2 Fractions
6.3 Non-negative Rational Numbers
6.4 Rational Numbers
6.5 Cauchy Sequences of Rational Numbers
6.6 Real Numbers
6.7 Sets of the Power of the Continuum
7. TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC
7.1 Transfinite Induction and Definition by Transfinite Recursion
7.2 Elements of Ordinal Arithmetic
7.3 Cardinal Numbers Again and Alephs
7.4 Well-Ordered Sets
7.5 Revised Summary of Axioms
8. THE AXIOM OF CHOICE
8.1 Some Applications of the Axiom of Choice
8.2 Equivalents of the Axiom of Choice
8.3 Axioms Which Imply the Axiom of Choice
8.4 Independence of the Axiom of Choice and the Generalized Continuum Hypothesis
REFERENCES
GLOSSARY OF SYMBOLS
AUTHOR INDEX
SUBJECT INDEX
Details
Erscheinungsjahr: 2003
Fachbereich: Grundlagen
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Kartoniert / Broschiert
ISBN-13: 9780486616308
ISBN-10: 0486616304
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Suppes, Patrick
Hersteller: Dover Publications Inc.
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 214 x 137 x 14 mm
Von/Mit: Patrick Suppes
Erscheinungsdatum: 28.03.2003
Gewicht: 0,304 kg
Artikel-ID: 131412873

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