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:
“Each in their double Eden closed
They fail to see the gardener there
Has planted Error....”
—Philip Larkin (1922–1986)
“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)