An Introduction to Elementary Set Theory

Abstract

We provide a student project on elementary set theory based on the original historical sources written by two key figures in the development of set theory: Georg Cantor and Richard Dedekind.  By taking excerpts from Cantor’s treatise Contributions to the Founding of the Theory of Numbers and Dedekind’s essay “The Nature and Meaning of Numbers” as source material, the project develops the basic properties of sets, and discusses how to define the size of a set and how to compare different sizes of sets. The project concludes by exploring a rather unusual world of infinite sets.  This project is a self-contained treatment of the topics from elementary set theory typically covered in a first course in discrete mathematics at a freshman or sophomore level. It may be used as a text for the set theory unit of such a course, and should require approximately three to four weeks of class time to complete. A first course in discrete mathematics typically covers logic, set theory, and number theory units. This project may be covered immediately after the unit on logic or at the end of the course when both logic and number theory have been covered. No specific prerequisites are assumed other than a basic familiarity with pre-calculus and/or college algebra.