Why is it that the set A={1/n:n is counting number} is not a closed set?(adsbygoogle = window.adsbygoogle || []).push({});

We see that no matter how small our ε is, ε-neighborhood will always contain a point not in A (one reason is that Q* is dense in ℝ), thus, all the elements in A is boundary point, and we know that by definition, if bd(A)≤A, then A is closed (this is what Steven R. Lay used in his book). (≤-subset). A good friend of mine told me that A does not contain cluster point and that made A not a closed set, he said (and i know) that closed set always contain cluster points. is this some sort of contradiction?

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# Point set topology

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