| 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 |
