Naive Set Theory

Paul R. Halmos

Every mathematician agrees they should have some knowledge of set theory, but where they diverge is in attempting to decide how much knowledge constitutes “some.” That question is addressed by Naive Set Theory, which provides the answer.

This book aims to introduce beginning students of advanced mathematics to the fundamental set-theoretic realities of existence in a manner that is as devoid as possible of philosophical discourse and logical formalism. This will allow the book to fulfill its aim. The reader is presented with an account from the perspective of an aspiring mathematician eager to learn about manifolds, integrals, and groups. When viewed from this angle, the ideas and procedures described in this book are essentially some of the standard mathematical tools; an experienced specialist will not learn anything new from reading this.

In a book solely concerned with explaining something, like this one, scholarly bibliographical credits and references are not appropriate. The student interested in set theory for its own sake should be aware, however, that this book only covers a small portion of the subject’s overall scope and that there is much more to learn about it. Hausdorff’s set theory is still considered one of the most elegant sources of set-theoretic wisdom. A new addition to the canon of published works, the Axiomatic set theory by Suppes is notable for its readability. It has a comprehensive bibliography that has been brought up to date.