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:
“The worst feature of this double consciousness is, that the two lives, of the understanding and of the soul, which we lead, really show very little relation to each other; never meet and measure each other: one prevails now, all buzz and din; and the other prevails then, all infinitude and paradise; and, with the progress of life, the two discover no greater disposition to reconcile themselves.”
—Ralph Waldo Emerson (1803–1882)
“What we commonly call man, the eating, drinking, planting, counting man, does not, as we know him, represent himself, but misrepresents himself. Him we do not respect, but the soul, whose organ he is, would he let it appear through his action, would make our knees bend.”
—Ralph Waldo Emerson (1803–1882)