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Author:   E Kamke ,  Frederick Bagemihl
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 17.70cm , Height: 1.60cm , Length: 22.10cm
Weight:   0.340kg
ISBN:  

9780486450834

ISBN 10:   048645083
Pages:   144
Publication Date:   10 February 2006
Audience:   General/trade ,  General
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

"INTRODUCTION CHAPTER I. THE RUDIMENTS OF SET THEORY 1. A First Classification of Sets 2. Three Remarkable Examples of Enumerable Sets 3. ""Subset, Sum, and Intersection of Sets; in Particular, of Enumerable Sets"" 4. An Example of a Nonenumerable Set CHAPTER II. ARBITRARY SETS AND THEIR CARDINAL NUMBERS 1. Extensions of the Number Concept 2. Equivalence of Sets 3. Cardinal Numbers 4. Introductory Remarks Concerning the Scale of Cardinal Numbers 5. F. Bernstein's Equivalence-Theorem 6. The Sum of Two Cardinal Numbers 7. The Product of Two Cardinal Numbers 8. The Sum of Arbitrarily Many Cardinal Numbers 9. The Product of Arbitrarily Many Cardinal Numbers 10. The Power 11. Some Examples of the Evaluation of Powers CHAPTER III. ORDERED SETS AND THEIR ORDER TYPES 1. Definition of Ordered Set 2. Similarity and Order Type 3. The Sum of Order Types 4. The Product of Two Order Types 5. Power of Type Classes 6. Dense Sets 7. Continuous Sets CHAPTER IV. WELL-ORDERED SETS AND THEIR ORDINAL NUMBERS 1. Definition of Well-ordering and of Ordinal Number 2. ""Addition of Arbitrarily Many, and Multiplication of Two, Ordinal Numbers"" 3. Subsets and Similarity Mappings of Well-ordered Sets 4. The Comparison of Ordinal Numbers 5. Sequences of Ordinal Numbers 6. Operating with Ordinal Numbers 7. ""The Sequence of Ordinal Numbers, and Transfinite Induction"" 8. The Product of Arbitrarily Many Ordinal Numbers 9. Powers of Ordinal Numbers 10. Polynomials in Ordinal Numbers 11. The Well-ordering Theorem 12. An Application of the Well-ordering Theorem 13. The Well-ordering of Cardinal Numbers 14. Further Rules of Operation for Cardinal Numbers. Order Type of Number Classes 15. Ordinal Numbers and Sets of Points CONCLUDING REMARKS BIBLIOGRAPHY KEY TO SYMBOLS INDEX"

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