Let S be an infinite subset of (the extended complex plane). Show that either S has a limit point in S or every Disc D'( ,r) (punctured disc) contains a point of S (so that is a limit point of S in the space ).

My argument so far is:

Assume S does not have a limit point in S. Then take an abitrary disc D'( ,r).

Now assume for contradiction D'( ,r) does not contain a point of S. But I can't see where I can find a contradiction to the first statement. Can someone help, or provide an alternative argument? Thanks