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**Chaobunny** 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 $\displaystyle $\exists$$ a limit point $\displaystyle p$ of $\displaystyle M$. Then all open intervals containing $\displaystyle p$ must contain an element of $\displaystyle M$ different from $\displaystyle p$. Consider an interval $\displaystyle I$ that contains $\displaystyle p$. If $\displaystyle p \in M$, then any such $\displaystyle I$ bounded by $\displaystyle (p-1, p+1)$ does not contain any other points of $\displaystyle M$ different from $\displaystyle p$ because no other integers lie in this range. If $\displaystyle p \notin M$, then any $\displaystyle I$ containing $\displaystyle p$ that is bounded by $\displaystyle (a, a+1)$ where $\displaystyle a \in M$ will not contain any elements of $\displaystyle M$ because no integers lie in this range. Thus, not every open interval containing $\displaystyle p$ contains a point of $\displaystyle M$ different from $\displaystyle p$, therefore no limit point of $\displaystyle M$ exists.