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pigeonhole principle
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(Theorem)
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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.
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"pigeonhole principle" is owned by djao.
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| Other names: |
box principle, Dirichlet principle |
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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 MSC: | 03E05 (Mathematical logic and foundations :: Set theory :: Other combinatorial set theory) |
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Pending Errata and Addenda
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