Set theory

Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. It is the language in which mathematical objects are described. It is (along with logic and the predicate calculus) the axiomatic foundations for mathematics, allowing mathematical objects to be constructed formally from the undefined terms of "set", and "set membership". And, it is, in its own right, a branch of mathematics and an active field of ongoing mathematical research.

Related Topics:
Set - Primary school - Logic - Predicate calculus - Foundations for mathematics - Mathematics

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Like the concepts of point and line in Euclidian geometry, in mathematics, the terms "set" and "set membership" are fundamental objects used to define other mathematical objects, and so are not themselves formally defined. In Naive set theory, sets are introduced and understood using, what is taken to be, the self-evident concept of sets as collections of objects considered as a whole. In modern formal axiomatic set theory, sets and set membership are undefined terms, described by postulating certain axioms, which specify their properties.

Related Topics:
Point - Line - Euclidian geometry - Naive set theory - Axiomatic set theory

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