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proof that a finite collection of sets will not suffice
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(Proof)
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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.
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"proof that a finite collection of sets will not suffice" is owned by rspuzio.
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Cross-references: contradiction, contains, union, length, translation, right, translate, place, cut
This is version 1 of proof that a finite collection of sets will not suffice, born on 2004-09-25.
Object id is 6234, canonical name is ProofThatAFiniteCollectionOfSetsWillNotSuffice.
Accessed 1085 times total.
Classification:
| AMS MSC: | 28E99 (Measure and integration :: Miscellaneous topics in measure theory :: Miscellaneous) |
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Pending Errata and Addenda
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