A point $\displaystyle \alpha$ is said to be a limit point of a set E of points in the complex plane (as opposed to a sequence $\displaystyle z_n$) if every neighborhood of $\displaystyle \alpha$ contains infinitely many (distinct) points of E. Show that a sequence $\displaystyle z_n$ can have a limit point $\displaystyle \alpha$ in the sense that, given any $\displaystyle \epsilon$ the inequality $\displaystyle |z_n - \alpha | < \epsilon$ holds for infinitely many points of $\displaystyle z_n$, without being a limit point of the set of points corresponding to the terms of $\displaystyle z_n$.