The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
A correspondence, also called a one-to-one correspondence or a bijection, is a function from a set X to a set Y that has the property that for any element y in Y there is a unique element x in X such that f(x) = y. Most mathematical definitions of equivalence are correspondences that preserve some structure. For example, two groups are equivalent if there exists a correspondence between them that preserves their group structures. If there exists a correspondence between two sets, then they are said to have the same cardinality. A set X is said to be infinite if there is a subset Y of X such that Y is not equal to X, Y is not empty, and there is a correspondence between X and Y. The idea of correspondence originated with Bernhard Bolzano in the 1850s and was used extensively by Georg Cantor in his study of cardinality, infinite sets, and ordinal numbers. Cantor revolutionized the mathematical concept of infinity, but his contemporaries were hostile to his ideas and failed to realize their significance. Nowadays, Cantor's arguments are used without hesitation, and correspondences are used frequently in every area of mathematics.