Definition:Bounded Sequence/Normed Vector Space/Unbounded

This page is about Unbounded Sequence in the context of Normed Vector Space. For other uses, see Unbounded.

Definition

Let $\struct {X, \norm {\, \cdot \,} }$ be a normed vector space.

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

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