Accumulation Point at Infinity? This is a follow up question to the one I posted here. So my new question involves accumulation points and infinity. Can infinity be considered an accumulation point? For example consider the following set 
$$S = \{ 2^n + \frac{1}{k} \space : \space n, k \in N \}$$
 Now if we fix $n$ the set tends to $2^n$ but if we fix $k$ the set tends to $\infty$. Does this mean that accumulation points exist at $2^n$ and $\infty$? Any help would be appreciated. 

The answer to the question is yes.
If you're talking about $+\infty$, as opposed to $-\infty$ and also as opposed to a single $\infty$ at both ends of the line, then a basic open neighborhood of $+\infty$ is a set of the form
$$
(a,+\infty] = \left\{ x\in\mathbb R\cup\{+\infty\} : x>a \right\} = \left\{ x\in\mathbb R\cup\{+\infty\} : (x\in\mathbb R\ \&\ x>a)\text{ or }x=+\infty \right\}.
$$
And an open neighborhood of $+\infty$ is any open set that has as a subset some basic open neighborhood of $+\infty$.
The point $+\infty$ is an accumulation point of a set $A$ precisely if every open neighborhood of $+\infty$ intersects $A$ at at least one point other than $+\infty$.
