This statement forms the basis of radix sort, while the Fubini principle states that, if there is an average of x packets in each one, at least one of this principle's namesake structures must have more than x items.
This statement can be used to prove that a sequence of integers with general term xn where n = ab + 1 contains at least one monotonic sequence with a + 1 terms, a specific case of Dilworth's Lemma. In addition to the Erdos-Szekeres Theorem, this statement is used to prove a regularity test for a language involving the ability to insert an arbitrary number of characters into a string, the pumping lemma. This statement forms the basis of radix sort, while the Fubini principle states that, if there is an average of x packets in each one, at least one of this principle's namesake structures must have more than x items. For ten points, name this principle that informally states that given x containers and more than x objects to place into those containers, one container must have more than one object, which was first stated by Dirichlet.
This statement can be used to prove that a sequence of integers with general term xn where n = ab + 1 contains at least one monotonic sequence with a + 1 terms, a specific case of Dilworth's Lemma.
{Pigeonhole} Principle [accept {Dirichlet's Box Principle} before “For {ten} points”]