In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which van Lint & Wilson (2001) call “one of the most important tools in combinatorics,” one describes a finite set X from two perspectives leading to two distinct expressions for the size of the set. Since both expressions equal the size of the same set, they equal each other.
Famous quotes containing the words double and/or counting:
“American families, however, without exception, experience a double message in our society, one that claims a commitment to families and stresses the importance of raising bright, stable, productive citizens, yet remains so bound by an ideal of “rugged individualism” that parents receive little support in their task from the public or private sectors.”
—Bernice Weissbourd (20th century)
“But counting up to two
Is harder to do....”
—Philip Larkin (1922–1986)