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set of ratoinals are not compact
Say your general interval is [x,y]. Since x max{ 1/(2(q-x)), [ 1/(2(y-q)) } We have q - 1/(2n) < q < q + 1/(2n) so there are rational numbers b and c such that q - 1/(2n) < b < q < c < q + 1/(2n). Then if O_n = [x,b)?(c,y] we have c-b < q + 1/(2n) - (q - 1/(2n)) = 1/n The O_n will be an open cover of the rationals in [x,y] with no finite subcover. source: yahoo ]
Expert answered|sharpies|Points 7389|
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Asked 4/15/2012 8:38:21 AM
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