Definition:Convergent Sequence/Normed Division Ring/Definition 2
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Definition
Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring.
Let $\sequence {x_n} $ be a sequence in $R$.
The sequence $\sequence {x_n}$ converges to the limit $x \in R$ in the norm $\norm {\, \cdot \,}$ if and only if:
- $\sequence {x_n}$ converges to $x$ in the metric induced by the norm $\norm {\, \cdot \,}$
Also see
- Definition:Metric Induced by Norm on Division Ring
- Metric Induced by Norm on Normed Division Ring is Metric