Set Theory
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Contents |
[edit] Introduction
Set theory is concerned with the concept of a set, essentially a collection of objects that we call elements. Because of its generality, set theory forms the foundation of every other part of mathematics.
[edit] Before You Begin
In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. (I hope to have some links to other Wikibooks here soon.)
- Mathematical Logic & Proofs
- Mathematics is all about proofs. One of the goals of this book is to improve your skills in doing proofs, but you will not learn any of the basics here.
- Many constructions in set theory are simply generalizations of constructions in mathematical logic, and therefore logic is a necessity of learning set theory.
[edit] How to Use This Book
A Wikibook is very different from a standard textbook, and this is simultaneously a great strength and a great weakness.
[edit] Set Theory
- Chapter 0. Introduction
- Chapter 1. Sets
- Chapter 2. Characteristic functions
- Chapter 2. Axioms
- Chapter 3. Relations
- Chapter 4. Orderings
- Chapter 5. Zorn's Lemma and the Axiom of Choice
- Chapter 6. Ordinals
- Chapter 7. Cardinals
- Chapter 8. Zermelo-Fraenkel Axiomatic Set Theory
- Appendix 1. Naive Set Theory
- Review
[edit] Help
[edit] Question & Answer
what is the set operation?
[edit] Further Reading
- Discrete mathematics/Set theory
- Krzysztof Ciesielski, Set Theory for the Working Mathematician (1997)
- P. R. Halmos, Naive Set Theory (1974)
- Karel Hrbacek, Thomas J. Jech, Introduction to set theory (1999)
- Thomas J. Jech, Set Theory 3rd Edition (2006)
- Kenneth Kunen, Set Theory: an introduction to independence proofs (1980)
- Judith Roitman, Introduction to Modern Set Theory (1990)
- John H. Conway, Richard Guy The Book of Numbers - chapter 10
- Tobias Dantzig, Joseph Mazur Number: The Language of Science
