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pigeonhole principle (Theorem)

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.




"pigeonhole principle" is owned by djao.
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Other names:  box principle, Dirichlet principle

Attachments:
example of pigeonhole principle (Example) by Mathprof
proof of pigeonhole principle (Proof) by Wkbj79
another proof of pigeonhole principle (Proof) by ratboy
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Cross-references: contains, theorem, proper subset, bijection, natural number
There are 10 references to this entry.

This is version 6 of pigeonhole principle, born on 2001-10-25, modified 2003-04-03.
Object id is 502, canonical name is PigeonholePrinciple.
Accessed 15152 times total.

Classification:
AMS MSC03E05 (Mathematical logic and foundations :: Set theory :: Other combinatorial set theory)

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