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Set theory is the mathematical theory of sets, which represent collections of abstract objects. It has a central role in modern mathematical theory, providing the basic language in which most of mathematics is expressed.

For more information on set theory in Wikipedia, see:

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.
Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's Paradox) in naive set theory.
Various versions of logic have associated sorts of sets (such as fuzzy sets in fuzzy logic).
Internal set theory an extension of axiomatic set theory that admits infinitesimal and illimited non-standard numbers.
Musical set theory concerns the application of combinatorics and group theory to music; beyond the fact that it uses finite sets it has nothing to do with mathematical set theory of any kind.

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* Discrete mathematics

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