Definition:Convergent Sequence/Normed Division Ring/Definition 2

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 $x \in R$ in the norm $\norm {\, \cdot \,}$ :


 * $\sequence {x_n}$ 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

Generalizations

 * Definition:Convergent Sequence in Metric Space