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 $A \setminus \left\{{\alpha}\right\}$.