# Definition:Convergent Sequence/Normed Division Ring/Definition 4

## 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 topology induced by the norm $\norm {\, \cdot \,}$