Definition:Bounded Sequence/Normed Division Ring
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This page is about Bounded Sequence in the context of Normed Division Ring. For other uses, see 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 $1.7$