Definition:Set Theory

Set Theory is the branch of mathematics which studies sets.

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.