proof that a finite collection of sets will not suffice

Suppose that you cut $[0,1]$ into $A_{0},...,A_{n}$ . 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 $\epsilon$ be the smallest translation length : if after translation the union contains $[0,1]$ , necessarily $[0,\epsilon]\subset A_{0}$ . A contradiction ensues.

Title	proof that a finite collection 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