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 |