# Set Theory

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 nearly 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 at making 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.

## Set theory

Introduction
Appendix 1. Naive Set Theory
Review

• 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