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 $\epsilon$ : $\forall a\in A, (a-\epsilon,a+\epsilon)\cap A=\varnothing$.
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 $\epsilon$ : $\forall a\in A, (a-\epsilon,a+\epsilon)\cap A=\varnothing$.