Definition:Convergent Sequence/Normed Division Ring/Definition 3

From ProofWiki
Jump to navigation Jump to search


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:

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

Also see