Category:Set Theory

Set Theory is the branch of mathematics which studies sets.

Definitions specific to this category can be found in Definitions/Set Theory.

There are several "versions" of set theory, all of which share the same basic ideas but whose foundations are completely different.

• Naive set theory is based upon an intuitive understanding of the various operations and relations which provide one with the tools to manipulate sets and their contents.

• Axiomatic set theory is based upon a rigorously defined set of axioms which are designed to ensure that no paradoxes are able to be defined. There are several such systems.

• Pure set theory is a system of set theory in which all elements of sets are themselves sets. Most systems of axiomatic set theory are designed in this way.

Sources

• Paul R. Halmos: Naive Set Theory (1960): Preface

... General set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some, and here it is; read it, absorb it, and forget it.

• Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (1993): $\S 1.1$

In set theory, there is really only one fundamental notion:

The ability to regard any collection of objects as a single entity (i.e. as a set).