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'pigeonhole principle'
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| Title of object: |
pigeonhole principle |
| Canonical Name: |
PigeonholePrinciple |
| Type: |
Theorem |
| Created on: |
2001-10-25 12:01:30-04 |
| Modified on: |
2001-10-25 12:08:14-04 |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
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Content:
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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