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I need to find the interior, accumulation points, closure, and boundary of the set

$$ A = \left\{ \frac1n + \frac1k \in \mathbb{R} \mid n,k \in \mathbb{N} \right\} $$ and use the information to determine whether the set is bounded, closed, or compact.


So far, I have that the interior is empty, but not sure how to prove it. My thoughts are to fix $n$ and then the accumulation points would be $\left\{ \frac 1n \mid n \in \mathbb{N} \right\}$. But I'm not sure if that is correct. Then, I believe that the boundary is $[0,2]$. Can someone confirm that?

Any help would be appreciated.

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    For the boundary, consider $\frac{7}{4}$, which is not in $A$ or in $A$'s boundary, so there must be a point in the boundary which is less than it but greater than or equal to $\frac12+\frac12$2012-10-05

2 Answers 2