Prove the following:
An accumulation point of a set S is either an interior point of S or a boundary point of S.
This seems very logical to me, I just dont know how to prove it.
I know that an accumulation point may or may not be in S.
If it is in S then it would be an interior and boundary. If it is not in S then it would be a boundary point. Pretty simple I think, but how can I actually prove this?