Definition:Bounded Sequence/Metric Space

Definition
Let $M$ be a metric space.

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

Then $\sequence {x_n}$ is a bounded sequence $\sequence {x_n}$ is bounded in $M$.

That is:
 * $\exists K \in \R: \forall n, m \in \N: \map d {x_n, x_m} \le K$