$p, p \in \mathbb{X}$ is a limit point of $\mathbb{E}, |\mathbb{E}| \le |\mathbb{X}|$ if every neighborhood of $p$ includes at least one element $q \not= p$ such that $q \in \mathbb{E}$.
It also says that the set $\mathbb{E}$ approaches to p.
In $\mathbb{R}$, set $\mathbb{X} = \frac{1}{n}, n \in \naturals$.
Any open ball of radius "r" includes a point of {$\frac{1}{n}, n \in \naturals$} because of arithmetical median.
0 is a limit point, note 0 is not in the set.
No other points except 0 is a limit point of $\mathbb{X}$.
A point $p, p \in \mathbb{R}$ is an interior point of set $\mathbb{S}$ if it has a neighborhood $\mathbb{X}$ is entirely inside $\mathbb{S}$.
If p is a limit point of $\mathbb{E}$, every neighborhood of p contains infinitely many points of $\mathbb{E}$.