Definition:Limit of Sequence/Normed Division Ring

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Definition

Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring.

Let $\sequence {x_n} $ be a sequence in $R$.

Let $\sequence {x_n}$ converge to $x \in R$.

Then $x$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity which is usually written:

$\displaystyle x = \lim_{n \mathop \to \infty} x_n$


Sources