Q:

How can I understand/visualise this (finite) set?

$$B_{\epsilon}=\left(\frac{\epsilon}{2}\Bbb Z\right)\cap [-1,1]$$
This is given as a hint for a question but its not of much help since I am not quite sure what this even is. 
The question is asking that I use this set to prove that 
$S_{\epsilon}=\{(y_n): y_n\in B_{\epsilon} \text{ and } y_n=0 \text{ }  \forall n>N_\epsilon\}\cap  S$  is a net for $S$ if $N_\epsilon$ is sufficiently large.

A:

That set contains all the numbers
$$
0, \pm\epsilon/2, \pm\epsilon, \pm 3\epsilon/2, \ldots
$$
that happen to like in the interval $[-1,1]$. It's a bunch of points spaced $\epsilon/2$ apart on the number line.
I havent't thought about the question it's a hint for the solution of.

