set theory

set theory

Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its terminology and concepts. These include the operations of union (∪), and intersection (∩). The union of two sets is a set containing all the elements of both sets, each listed once. The intersection is the set of all elements common to both original sets. Set theory is useful in analyzing difficult concepts in mathematics and logic. It was placed on a firm theoretical footing by Georg Cantor, who discovered the value of clearly formulated sets in the analysis of problems in symbolic logic and number theory.

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The branch of mathematics or logic that is concerned with sets of objects and rules for their manipulation. UNION, INTERSECT and COMPLEMENT are its three primary operations and they are used in relational databases as follows.

Given a file of Americans and a file of golfers, UNION would create a file of all Americans and golfers. INTERSECT would create a file of American golfers, and COMPLEMENT would create a file of golfers who are not Americans, or of Americans who are not golfers. See fuzzy logic.

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(mathematics)

set theory - A mathematical formalisation of the theory of "sets" (aggregates or collections) of objects ("elements" or "members"). Many mathematicians use set theory as the basis for all other mathematics. Mathematicians began to realise toward the end of the 19th century that just doing "the obvious thing" with sets led to embarrassing paradoxes, the most famous being Russell's Paradox. As a result, they acknowledged the need for a suitable axiomatisation for talking about sets. Numerous such axiomatisations exist; the most popular among ordinary mathematicians is Zermelo Fränkel set theory. The beginnings of set theory.