View source for Convergence in norm

{{MSC|46Bxx}}
{{TEX|done}}

Convergence of a sequence $(x_n)$ in a normed vector space $X$ to an element $x$, defined in the following way: $x_n \rightarrow x$ if 
$$
\text{$\left\| x_n - x \right\| \rightarrow 0$ as $n\rightarrow\infty$.}
$$
Here $\left\|\cdot\right\|$ is the norm in $X$.

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See also [[Convergence, types of|Convergence, types of]].