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:
“Go; and if that word have not quite killed thee,
Ease me with death by bidding me got too.
Oh, if it have, let my word work on me,
And a just office on a murderer do.
Except it be too late to kill me so,
Being double dead: going, and bidding go.”
—John Donne (1572–1631)
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—Amaru (c. seventh century A.D.)