If A is a subset of the topological space X, and x is in X, then x is a limit point (or cluster point )of A if every neightborhood of x intersects A in some point other than x itself

or

x is a limit point of A if it belongs to the closure of A-{x} (x may or may not have to lie in A)

When doing proofs, it's often more helpful to use the definition like how I used it below: