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Does the set A= {$1+\frac{(-1)^n}{n}:0\leq n\leq10,n\in\mathbb{N}$} have any accumulation points in $\mathbb{R}$?

My guess is no since this is a finite set.
So there exist $\epsilon$ : $\forall a\in A, (a-\epsilon,a+\epsilon)\cap A=\varnothing$.

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    Any finite set has no accumulation point, you're right.2012-01-25
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    What is $A$? Is it the set you defined?2012-01-25
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    Why do you guess that? There is a great chance that the evidence that lead you to conjecture that will lead to an actual proof. It is impossible to know, until you tell us.2012-01-25
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    Your guess is correct, but the statement that follows it is clearly false: $(a-\epsilon,a+\epsilon)\cap A$ cannot be empty, as it certainly includes $a$. Do you mean $(a-\epsilon,a+\epsilon)\cap(A\setminus\{a\})$?2012-01-25
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    $1+\frac{(-1)^0}{0}$ is not usually regarded as a real number.2012-01-26
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    @Henry: Or even as an imaginary one!2012-01-26

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