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 diverges from that of a limit point of a set, in that for a limit point it is necessary that every neighborhood of contains at least one point of Thus every limit point is an adherent point, but the reverse is not valid.