# Definition:Bounded Sequence/Normed Division Ring

< Definition:Bounded Sequence(Redirected from Definition:Bounded Sequence in Normed Division Ring)

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*This page is about sequences in normed division rings which are bounded. For other uses, see Definition:Bounded.*

## Definition

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

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

Then $\sequence {x_n}$ is **bounded** if and only if:

- $\exists K \in \R$ such that $\forall n \in \N: \norm {x_n} \le K$

### Unbounded

$\sequence {x_n}$ is **unbounded** if and only if it is not bounded.

## Sources

- 2007: Svetlana Katok:
*p-adic Analysis Compared with Real*... (previous) ... (next): $\S 1.2$: Normed Fields, Definition $1.7$