Definition:Cauchy Sequence/Rational Numbers

Definition
Let $\left \langle {x_n} \right \rangle$ be a rational sequence.

Then $\left \langle {x_n} \right \rangle$ is a Cauchy sequence iff:
 * $\forall \epsilon \in \Q_{>0}: \exists N \in \N: \forall m, n \in \N: m, n \ge N: \left|{x_n - x_m}\right| < \epsilon$

where $\Q_{>0}$ denotes the set of all strictly positive rational numbers.

Considering the set of rational numbers as a metric space, it is clear that this is a special case of the definition for a metric space.