naive set theory

In the discussion of the foundations of mathematics, several set theories have been developed, of which naive set theory is one. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and the everyday usage of set theory concepts in most contemporary mathematics.
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See also naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. This book is an undergraduate introduction to not-very-naive set theory which has lasted for decades. It is still considered by many to be the best introduction to set theory for beginners. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo-Fraenkel set theory and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: There are no long-winded discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals. Instead, it tries to be intelligible to someone who has never thought about set theory before.
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