proof that a finite collection of sets will not suffice
Suppose that you cut into .
Displacing the parts is simply translating them; you can suppose
that you leave in place and translate all the others to the
right. Let be the smallest translation
length : if after
translation the union contains , necessarily . A contradiction
ensues.
Title | proof that a finite collection![]() |
---|---|
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 |