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:
“To be a woman and a writer
is double mischief, for
the world will slight her
who slights “the servile house,” and who would rather
make odes than beds.”
—Dilys Laing (1906–1960)
“If you’re counting my eyebrows, I can help you. There are two.”
—Billy Wilder (b. 1906)