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 |