Banach space
Set
| context | $V$ … normed $F$-vector space |
| definiendum | $\mathcal V \in \mathrm{it}$ |
| forall | $v\in \mathrm{CauchySeq}(V)$ |
| postulate | $\exists v_\infty.\,\mathrm{lim}_{n\to\infty}\Vert v_n-v_\infty \Vert = 0$ |
Elaboration
For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm. $\Longleftrightarrow$ The space $\mathcal V$ is complete.
Reference
Wikipedia: Banach space
Requirements
Subset of
