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Klappentext Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." - School Science and Mathematics. Inhaltsverzeichnis INTRODUCTIONCHAPTER I. THE RUDIMENTS OF SET THEORY1. A First Classification of Sets2. Three Remarkable Examples of Enumerable Sets3. "Subset, Sum, and Intersection of Sets; in Particular, of Enumerable Sets"4. An Example of a Nonenumerable SetCHAPTER II. ARBITRARY SETS AND THEIR CARDINAL NUMBERS1. Extensions of the Number Concept2. Equivalence of Sets3. Cardinal Numbers4. Introductory Remarks Concerning the Scale of Cardinal Numbers5. F. Bernstein's Equivalence-Theorem6. The Sum of Two Cardinal Numbers7. The Product of Two Cardinal Numbers8. The Sum of Arbitrarily Many Cardinal Numbers9. The Product of Arbitrarily Many Cardinal Numbers10. The Power11. Some Examples of the Evaluation of PowersCHAPTER III. ORDERED SETS AND THEIR ORDER TYPES1. Definition of Ordered Set2. Similarity and Order Type3. The Sum of Order Types4. The Product of Two Order Types5. Power of Type Classes6. Dense Sets7. Continuous SetsCHAPTER IV. WELL-ORDERED SETS AND THEIR ORDINAL NUMBERS1. Definition of Well-ordering and of Ordinal Number2. "Addition of Arbitrarily Many, and Multiplication of Two, Ordinal Numbers"3. Subsets and Similarity Mappings of Well-ordered Sets4. The Comparison of Ordinal Numbers5. Sequences of Ordinal Numbers6. Operating with Ordinal Numbers7. "The Sequence of Ordinal Numbers, and Transfinite Induction"8. The Product of Arbitrarily Many Ordinal Numbers9. Powers of Ordinal Numbers10. Polynomials in Ordinal Numbers11. The Well-ordering Theorem12. An Application of the Well-ordering Theorem13. The Well-ordering of Cardinal Numbers14. Further Rules of Operation for Cardinal Numbers. Order Type of Number Classes15. Ordinal Numbers and Sets of PointsCONCLUDING REMARKSBIBLIOGRAPHYKEY TO SYMBOLSINDEX...
