\begin{definition}[Definition:Limit Point/Normed Vector Space/Sequence]
Let $M = \struct {X, \norm {\, \cdot \,}}$ be a normed vector space.
Let $Y \subseteq X$ be a subset of $X$.
Let $L \in Y$.
Let $\sequence {x_n}_{n \mathop \in \N}$ be a sequence in $Y \setminus \set L$.
Let $\sequence {x_n}_{n \mathop \in \N}$ converge to $L$. 
Then $L$ is a '''limit of  $\sequence {x_n}_{n \mathop \in \N}$ as $n$ tends to infinity''' which is usually written:
:$\ds L = \lim_{n \mathop \to \infty} x_n$
\end{definition}