Definition:Limit Point/Normed Vector Space/Sequence

Definition
Let $\tuple {X, \norm {\, \cdot \,}}$ be a normed vector space.

Let $Y \subseteq X$.

Let $\sequence {x_n}_{n \mathop \in \N}$ be a sequence in $Y$.

Let $\sequence {x_n}_{n \mathop \in \N}$ converge $L \in Y$.

Then $L$ is a limit of $\sequence {x_n}_{n \mathop \in \N}$ as $n$ tends to infinity which is usually written:
 * $\displaystyle L = \lim_{n \mathop \to \infty} x_n$