This definition differs from that of a limit point of a set, in that for a limit point it is required that every neighborhood of  contains at least one point of    Thus every limit point is an adherent point, but the converse is not true.
This definition contrasts with the concept of a limit point of a set in that for a limit point it is essential that every neighborhood of contains at least one point from Thus every limit point is an adherent point, but the opposite is not necessarily valid.