Well I don't want to specifically ask for the answer to this question, but there is no way to get around it. When we are talking about neighborhoods around an integer in the set of integers, do the radii of these neighborhoods necessarily have to be integers themselves. My thoughts would be no since the radius is defined as any $\epsilon$ > 0 but I wanted to make sure. Also, I suppose it is possible for a set to have no limit points, are the integers and example of this. Is a set with no limit points considered closed?

Thank you.