# proof that a finite collection of sets will not suffice

Suppose that you cut $[0,1]$ into ${A}_{0},\mathrm{\dots},{A}_{n}$.
Displacing the parts is simply translating them; you can suppose
that you leave ${A}_{0}$ in place and translate^{} all the others to the
right. Let $\u03f5$ be the smallest translation^{} length : if after
translation the union contains $[0,1]$, necessarily $[0,\u03f5]\subset {A}_{0}$. A contradiction^{} ensues.

Title | proof that a finite collection^{} of sets will not suffice |
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Canonical name | ProofThatAFiniteCollectionOfSetsWillNotSuffice |

Date of creation | 2013-03-22 14:38:46 |

Last modified on | 2013-03-22 14:38:46 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 4 |

Author | rspuzio (6075) |

Entry type | Proof |

Classification | msc 28E99 |