Definition:Limit of Sequence/Normed Vector Space

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Definition

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

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

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


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

$\displaystyle L = \lim_{n \mathop \to \infty} x_n$


Sources