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Set Theory

Applications Of Set Theory

Because of its very general or abstract nature, set theory has many applications in other branches of mathematics. In the branch called analysis, of which differential and integral calculus are important parts, an understanding of limit points and what is meant by the continuity of a function are based on set theory. The algebraic treatment of set operations leads to boolean algebra, in which the operations of intersection, union, and difference are interpreted as corresponding to the logical operations "and," "or," and "not," respectively. Boolean algebra in turn is used extensively in the design of digital electronic circuitry, such as that found in calculators and personal computers. Set theory provides the basis of topology, the study of sets together with the properties of various collections of subsets.

Resources

Books

Buxton, Laurie. Mathematics for Everyone. New York: Schocken Books, 1985.

Dauben, Joseph Warren. Georg Cantor: His Mathematics and Philosophy of the Infinite. Cambridge: Harvard University Press, 1979.

Eves, Howard Whitley. Foundations and Fundamental Concepts of Mathematics. NewYork: Dover, 1997.

Mandlebrot, Benoit B. The Fractal Geometry of Nature. New York: W. H. Freeman, 1983.


Periodicals

Moore, A. W. "A Brief History of Infinity." Scientific American 272, No. 4 (1995): 112-16.


J. R. Maddocks

KEY TERMS

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Complement

—That part of a set S which is not contained in a particular subset T. Written T', the union of T and T' equal S.

Difference

—The difference between two sets S and T, written ST is that part of S which is not in T.

Dimension

—A measure of the spatial extent of a set.

Element

—Any member of a set. An object in a set.

Intersection

—The intersection of two sets is itself a set comprised of all the elements common to both sets.

Set

—A set is a collection of things called members or elements of the set. In mathematics, the members of a set will often be numbers.

Subset

—A set, S, is called a subset of another set, I, if every member of S is contained in I.

Union

—The union of two sets is the set that contains all the elements found in either of both of the two sets.

Additional topics

Science EncyclopediaScience & Philosophy: Semiotics to SmeltingSet Theory - Definitions, Properties, Operations, Applications Of Set Theory