Difference between revisions of "Dirichlet box principle"
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| + | 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|Dirichlet theorem]] in the theory of Diophantine approximations). | ||
Latest revision as of 19:35, 5 June 2020
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=16845
Dirichlet box principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet_box_principle&oldid=16845
This article was adapted from an original article by V.G. Sprindzhuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article