Set Theory - eMyTextBooks

Set Theory

< Wikiversity < Wikiversity:School of Mathematics < School of Mathematics:Pure Mathematics

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.

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.

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.

Set Theory

• Chapter 0. Naive Set Theory
• Chapter 1. Axioms
• Chapter 2. Set Operations
• Chapter 3. Relations
• Chapter 4. Orderings
• Chapter 5. Zorn's Lemma and the Axiom of Choice
• Chapter 6. Ordinals
• Chapter 7. Cardinals

Help

Question & Answer

Have a question? Why not ask the very textbook that you are learning from?

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 (2002)
• Kenneth Kunen, Set Theory: an introduction to independence proofs (1980)

External Links