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 next war will be a war in which people not armies will suffer, and our boasted, hard-earned civilization will do us no good. Cannot the women rise to this great opportunity and work now, and not have the double horror, if another war comes, of losing their loved ones, and knowing that they lifted no finger when they might have worked hard?”
—Eleanor Roosevelt (1884–1962)
“If you’re counting my eyebrows, I can help you. There are two.”
—Billy Wilder (b. 1906)