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Is it true that for any uncountable subset T of $\mathbb R$, one can find a subset S of T such that S is countable. If yes, how can we prove it?

Thanks!

Edit: Is there a countable subset S of T such that for every element $t\in T$, there exists $s\in S$ such that $s\geq t$?

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    Just take $S$ to be one element of $T$?2012-09-23
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    My question was really stupid. It's not exactly what I wanted to say. Thank you!2012-09-23
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    There is no such thing has a stupid question. Sometimes you stumble on a question that is really easy just because you are trying to hard prove something where there isn't really something to prove2012-09-23
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    Yes I guess you are right. Thank you!2012-09-23
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    @alabama78 What exactly did you want to say?2012-09-23
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    @alabama78: my advice if you realised you asked the wrong question would be to ask a new question, rather than fix the old one. Unfortunately you now have answers to both the old and new questions, so there's not much you can do, but it's worth keeping in mind anyway.2012-09-23

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