Isolated Point

A point $a \in A$ is an isolated point of $A$ if it is not a Limit Point of $A$ . Namely, $\exists ε > 0 (V_{ε} (a) \cap A = \emptyset \lor {x})$ .

The definition here is to avoid the case in the limit pointer where we have the sequence $(a, a, a, \dots)$ , since that is technically a limit point.