okay so this is what is confusing me in this example: the definition of frontier point of a set $S$ is "every nbhd of $a$ contains both points in $S$ and points not in $S$. "
So in my mind I am picturing a number line, with the points as you would expect for the integers. I can take nbhds that don't contain any points of the integers except for the point $a$ itself. So are you saying the point $a$ itself is sufficient to satisfy the definition?