Definition:Limit of Sequence/Topological Space

Definition
Let $$X$$ be a topological space.

Let $$A \subseteq X$$.

Let $$\left \langle {x_n} \right \rangle$$ be a sequence in $$A$$ whose limit is $$\alpha$$.

Then $$\alpha$$ is a limit point of $$\left \langle {x_n} \right \rangle$$.

Some sources insist that $$\left \langle {x_n} \right \rangle$$ be a sequence in $$A \setminus \left\{{\alpha}\right\}$$.