Introduction to Proofs with Set Theory

Daniel Ashlock was awarded a Ph.D. in Mathematics from the California Institute of Technology. He has taught more than 50 different classes from abstract algebra to bioinformatics but enjoys set theory because it is the first time most students meet abstract mathematics. Dr. Ashlock is a Professor of Mathematics at the University of Guelph where he uses mathematics to help biologists with their research as well as continuing his own work in how to represent information to make it easier to understand and easier to work with on a computer. Dr. Ashlock is a Senior Member of the IEEE and has chaired technical committees in both bioinformatics and games, demonstrating the broad usefulness of an education in mathematics.Colin Lee received his Ph.D. in Applied Mathematics from the University of Guelph. While at the University of Guelph he taught set theory both initially as a teaching assistant for Dr. Daniel Ashlock, as well as subsequently as a lecturer in his own right. Since graduating he has been sporadically involved in mathematical research, education, and tutoring while pursuing a variety of endeavours including consulting, programming, commercial art, and authoring mystery and horror fiction.

• Preface.- Acknowledgments.- Introduction and Review of Background Material.- Boolean Logic and Truth (Values).- Quantified Predicates, Rules of Inference, and Arguments.- Mathematical Proofs.- Intuitive Set Theory.- Mathematical Induction.- Functions.- The Integers and Beyond.- Counting Things.- Relations.- Number Bases, Number Systems, and Operations.- Many Infinities: Cardinal Numbers.- Many Infinities: Ordinal Numbers.- Paradoxes and Axiomatic Set Theory.- Bibliography.- Authors' Biographies.- Index.