Set Theory

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 Axiomatic Set Theory , the concepts of sets and set membership are defined indirectly by first postulating certain Axiom s which specify their properties. In this conception, sets and set membership are fundamental concepts like Point and Line in Euclidean Geometry , and are not themselves directly defined.

SEE ALSO

List Of Set Theory Topics

Set gives a basic introduction to elementary set theory.

Naive Set Theory is the original set theory developed by mathematicians at the end of the 19th century.

Zermelo Set Theory is the theory developed by the German mathematician Ernst Zermelo .

Zermelo-Fraenkel Set Theory is the most commonly used system of axioms, based on Zermelo set theory and further developed by Abraham Fraenkel and Thoralf Skolem .

Axiomatic Set Theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's Paradox ) in naïve set theory.

New Foundations and Positive Set Theory are among the Alternative Set Theories which have been proposed.

Internal Set Theory is an extension of axiomatic set theory that admits Infinitesimal and illimited ''non-standard'' numbers.

Various versions of Logic have associated sorts of sets (such as Fuzzy Set s in Fuzzy Logic ).

Musical Set Theory concerns the application of Combinatorics and Group Theory to music; beyond the fact that it uses Finite Set s it has nothing to do with mathematical set theory of any kind. In the last two decades, Transformational Theory in music has taken the concepts of mathematical set theory more rigorously (see Lewin 1989).

	CATEGORIES ABOUT SET THEORY

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	formal methods

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Set Theory