This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Undergraduate students interested in set theory.
Elements of Set Theory, 1st Edition
List of Symbols
Chapter 1 Introduction
Baby Set Theory
Sets—An Informal View
Chapter 2 Axioms and Operations
Arbitrary Unions and Intersections
Algebra of Sets
Chapter 3 Relations and Functions
Infinite Cartesian Products
Chapter 4 Natural Numbers
Recursion on ?
Ordering on ?
Chapter 5 Construction of the Real Numbers
Chapter 6 Cardinal Numbers and the Axiom of Choice
Ordering Cardinal Numbers
Axiom of Choice
Arithmetic of Infinite Cardinals
Chapter 7 Orderings and Ordinals
Chapter 8 Ordinals and Order Types
Transfinite Recursion Again
Arithmetic of Order Types
Chapter 9 Special Topics
Appendix Notation, Logic, and Proofs
Selected References for Further Study
List of Axioms