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.
In algebra, a binary operation is a rule for combining the elements of a set two at a time. In most important examples that combination is also another member of the same set. Addition, subtraction, multiplication, and division are familiar binary operations. A familiar example of a binary operation that is associative (obeys the associative principle) is addition (+) of real numbers. For example, the sum of 10, 2, and 35 is determined equally as well as (10 + 2) + 35 = 12 + 35 = 47, or 10 + (2 + 35) = 10 + 37 = 47. The parentheses on either side of the defining equation indicate which two elements are to be combined first. Thus, the associative property states that combining a with b first, and then combining the result with c, is equivalent to combining b with c first, and then combining a with that result. A binary operation (*) defined on a set S obeys the associative property if (a * b) * c = a * (b * c), for any three elements a, b, and c in S. Multiplication of real numbers is another associative operation, for example, (5 x 2) x 3 = 10 x 3 = 30, and 5 x (2 x 3) = 5 x 6 = 30. However, not all binary operations are associative. Subtraction of real numbers is not associative since in general (a - b) -c not equal a - (b - c), for example (35 - 2) - 6 = 33 - 6 = 27, while 35 - (2 - 6) = 35 - (-4) = 39. Divisionof real numbers is not associative either. When the associative property holds for all the members of a set, every combination of elements must result in another element of the same set.