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## Homework Statement

Prove that the rationals as a subset of the reals can all be contained in open intervals the sum of whose width is less than any \epsilon > 0.

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Prove that the rationals as a subset of the reals can all be contained in open intervals the sum of whose width is less than any \epsilon > 0.

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Dick

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Dick

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Much better, thanks. Can you write a series that converges to epsilon? If you can write a series that sums to say, 1, you should be able to write a series that converges to epsilon.

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hmmm, like epsilon/(n^2+n)??

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Dick

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Sure, that works. I would have said sum epsilon*(1/2)^n. But whatever you like.hmmm, like epsilon/(n^2+n)??

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