pigeonhole principle

For any natural number $n$, there does not exist a bijection between $n$ and a proper subset of $n$.

The name of the theorem is based upon the observation that pigeons will not occupy a pigeonhole that already contains a pigeon, so there is no way to fit $n$ pigeons in fewer than $n$ pigeonholes.

Title	pigeonhole principle
Canonical name	PigeonholePrinciple
Date of creation	2013-03-22 11:53:32
Last modified on	2013-03-22 11:53:32
Owner	djao (24)
Last modified by	djao (24)
Numerical id	11
Author	djao (24)
Entry type	Theorem
Classification	msc 03E05
Classification	msc 03B22
Classification	msc 03-01
Classification	msc 03-00
Synonym	box principle
Synonym	Dirichlet principle