I've been really struggling with this question.
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Let {[x_j,y_j]}_(j>=0) be a sequence of closed, bounded intervals in R, with x_j<=y_j for all j>=1.
Suppose that the intervals which make up this sequence are disjoint, i.e. [x_j,y_j]∩[x_k,y_k] = Ø for j≠k.
Is it possible that R=U_(k>=1) [x_k,y_k]?
Hint: What sort of subset in R must be then be formed by the endpoints U_(k>=1) {x_k,y_k}
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Thank you so much!
2007-12-18
13:30:26
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2 answers
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asked by
Theodore E
1
in
Mathematics