Thank you for the help, the examples make sense. So I have thought this through a little more and I get what you are saying, now I am just trying to word it properly. Tell me how this sounds:

Solution: Assume that

a limit point

of

. Then all open intervals containing

must contain an element of

different from

. Consider an interval

that contains

. If

, then any such

bounded by

does not contain any other points of

different from

because no other integers lie in this range. If

, then any

containing

that is bounded by

where

will not contain any elements of

because no integers lie in this range. Thus, not every open interval containing

contains a point of

different from

, therefore no limit point of

exists.