Set theory

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 AskFactMaster.Com, 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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