Definition:Convergent Sequence/Normed Division Ring/Definition 3

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

the real sequence $\sequence {\norm {x_n - x} }$ converges to $0$ in the reals $\R$


Also see


Sources