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:
“What happens is that, as with drugs, he needs a stronger shot each time, and women are just women. The consumption of one woman is the consumption of all. You can’t double the dose.”
—Ian Fleming (1908–1964)
“But counting up to two
Is harder to do....”
—Philip Larkin (1922–1986)