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Reference.org
Double counting (proof technique)
open-in-new
<p>In <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a>, double counting, also called counting in two ways, is a <a href="/facts/Combinatorial_proof/EmUsc3H1">combinatorial proof</a> technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one <a href="/facts/Set_(mathematics)/BfucfHMq">set</a>. In this technique, which van Lint & Wilson (2001) call "one of the most important tools in combinatorics", one describes a <a href="/facts/Finite_set/za1newlP">finite set</a> 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. </p>