Dirichlet box principle
A theorem according to which any sample of $ n $ sets containing in total more than $ n $ elements comprises at least one set with at least two elements. Dirichlet's box principle can be formulated in a most popular manner as follows: If $ n $" boxes" contain $ n + 1 $" objects" , then at least one "box" contains at least two "objects" . The principle is frequently used in the theory of Diophantine approximations and in the theory of transcendental numbers to prove that a system of linear inequalities can be solved in integers (cf. Dirichlet theorem in the theory of Diophantine approximations).
Dirichlet box principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_box_principle&oldid=46715