# Dirichlet box principle

From Encyclopedia of Mathematics

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).

**How to Cite This Entry:**

Dirichlet box principle.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_box_principle&oldid=46715

This article was adapted from an original article by V.G. Sprindzhuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article