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Show that every uncountable set of real numbers has a point of accumulation.

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Okay. I've shown that. Oh, you wanted me to post an answer too? –  Asaf Karagila Oct 22 '12 at 20:49
    
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Instead of just demanding us to show something, how about stating what your own efforts have been so far? –  Hagen von Eitzen Oct 22 '12 at 21:41

1 Answer 1

up vote 6 down vote accepted

Hint:

If $A$ is an uncountable set of real numbers then there exists $k\in\mathbb Z$ such that $A\cap[k,k+1]$ is infinite. Use the definition of compactness, and the fact $[k,k+1]$ is a closed and bounded interval.

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