# 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 PigeonholePrinciple 2013-03-22 11:53:32 2013-03-22 11:53:32 djao (24) djao (24) 11 djao (24) Theorem msc 03E05 msc 03B22 msc 03-01 msc 03-00 box principle Dirichlet principle