Definition:Bounded Sequence/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