Definition:Bounded Sequence/Normed Vector Space

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

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

Then $\sequence {x_n}$ is bounded :
 * $\exists K \in \R$ such that $\forall n \in \N: \norm {x_n} \le K$