As stated in the title: Why can't a closed interval $[a,b]$ on R be written as the disjoint union of countably infinite many closed intervals $[a_i,b_i]$?
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$\begingroup$ Bounded both above and below? $\endgroup$– Tim RaczkowskiJun 8, 2015 at 16:08
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$\begingroup$ That's what bounded means, @TimRaczkowski In any event, what is an unbounded closed interval $[a,b]$ in $\mathbb R$? $\endgroup$– Thomas AndrewsJun 8, 2015 at 16:10
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1$\begingroup$ @ThomasAndrews Yes, I know that's what bounded means. I was making sure that the OP understood that. $\endgroup$– Tim RaczkowskiJun 8, 2015 at 16:14
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