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I am stuck on the last problem of my complex variable homework.

The problem is given the set $S=\{\frac{i}{n} \mid n \text{ is an integer}\}$,

a.) List the points in $S$.

b.) What are the accumulation points of $S$?

So far I have the points being $i$, $i/2$, $i/3,\ldots , i/n$ but that seems like it is too easy for this class.

Am I missing something?

The second part, I would think there are not any accumulation points because none of the neighborhoods of the points will include any other points for a small neighborhood.

Any help would be appreciated.

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    I believe the only accumulation point would be 0 since every neighborhood around 0 will contain a point in S(as n gets very large)2011-10-11
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    An accumulation point does not have to be in the set itself; it can be in the "larger" space we are considering, which in this case is presumably the set of all complex numbers.2011-10-11
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    I don't like the problem statement. 1. Zero is an integer, so your "set" contains $i/0$, which is a bit of a worry. 2. In a), you ask about $S$, which you haven't defined. I take it $S$ is that set from your previous sentence? As to what you are missing, you seem to be missing that the integers do not stop at $n$, but go on forever, so there are infinitely many points in $S$, not just $n$ points, as you have written.2011-10-11
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    Is the number $i$ fixed?2011-10-11
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    @GerryMyerson I agree that this would make more sense for the set S to only include positive integers or exclude 0. The answer I have so far for a.) +-i, +-i/2, +-i/3, ... b.) The only accumulation point would be zero as every neighborhood around zero would include a point in the set if we let n approach infinity.2011-10-11
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    Joe, that looks good to me.2011-10-11

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