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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).