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:
“Today, San Francisco has experienced a double tragedy of incredible proportions. As acting mayor, I order an immediate state of mourning in our city. The city and county of San Francisco must and will pull itself together at this time. We will carry on as best as we possibly can.... I think we all have to share the same sense of shame and the same sense of outrage.”
—Dianne Feinstein (b. 1933)
“Is it not manifest that our academic institutions should have a wider scope; that they should not be timid and keep the ruts of the last generation, but that wise men thinking for themselves and heartily seeking the good of mankind, and counting the cost of innovation, should dare to arouse the young to a just and heroic life; that the moral nature should be addressed in the school-room, and children should be treated as the high-born candidates of truth and virtue?”
—Ralph Waldo Emerson (1803–1882)