proof that a finite collection of sets will not suffice

Suppose that you cut [0,1] into A0,,An. Displacing the parts is simply translating them; you can suppose that you leave A0 in place and translateMathworldPlanetmath all the others to the right. Let ϵ be the smallest translationMathworldPlanetmathPlanetmath length : if after translation the union contains [0,1], necessarily [0,ϵ]A0. A contradictionMathworldPlanetmathPlanetmath ensues.

Title proof that a finite collectionMathworldPlanetmath of sets will not suffice
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