1. Elementary Logic
1.1 Statements and Their Connectives
1.2 Three More Connectives
1.3 Tautology, Implication, and Equivalence
1.4 Contradiction
1.5 Deductive Reasoning
1.6 Quantification Rules
1.7 Proof of Validity
1.8 Mathematical Induction
2. The Concept of Sets
2.1 Sets and Subsets
2.2 Specification of Sets
2.3 Unions and Intersections
2.4 Complements
2.5 Venn Diagrams
2.6 Indexed Families of Sets
2.7 The Russell Paradox
2.8 A History Remark
3. Relations and Functions
3.1 Cartesian Product of Two Sets
3.2 Relations
3.3 Partitions and Equivalence Relations
3.4 Functions
3.5 Images and Inverse Images of Sets
3.6 Injective, Surjective, and Bijective Functions
3.7 Composition of Functions
4. Denumerable Sets and Nondenumerable Sets
4.1 Finite and Infinite Sets
4.2 Equipotence of Sets
4.3 Example and Properties of Denumerable Sets
4.4 Nondenumerable Sets
5. Cardinal Numbers and Cardinal Arithmetic
5.1 The Concept of Cardinal Numbers
5.2 Ordering of the Cardinal Numbers-The Schroder Bernstein Theorem
5.3 Cardinal Number of a Power Set-Cantos Theorem
5.4 Addition of Cardinal Numbers
5.5 Multiplication of Cardinal Numbers
5.6 Exponentiation of Cardinal Numbers
5.7 Further Examples of Cardinal Numbers
5.8 The Contonuum Hypothesis and Its Generaliztion
6. The Axiom of Choice and Some of Its Equivalent Forms
6.1 Introduction
6.2 The Hausdorff Maximality Principle
6.3 Zons Lemma
6.4 The Well-Ordering Principle
6.5 The Principle of Transfinite Induction
6.6 Historical Remarks
7. Ordinal Numbers and Ordinal Arithmetic
7.1 The Concept of Ordinal Numbers
7.2 Ordering of the Ordinal Numbers
7.3 Addition of Ordinal Numbers
7.4 Multiplication of Ordinal Numbers
7.5 Conclusion
Appendix/The Peano Axioms for Natural Numbers
Answers to Selected Problems
Glossary of Symbols and Abbreviations
Selected Bibliography
Index
