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Well, the empty set contains each and every dark number, that's for sure!Wrong. The sequences (E(1)∩E(2)∩...∩E(n)) and (E(n)) have precisely the same terms and therefore it is impossible that only one of them gets empty. If you prove that all endsegments are infinite, then you miss the dark numbers which are required to empty the endsegments in accordance with the empty intersection.
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