Definition:Convergent Sequence/Rational Numbers

Definition
Let $\left \langle {x_k} \right \rangle$ be a sequence in $\Q$.

$\left \langle {x_k} \right \rangle$ converges to the limit $l \in \R$ :


 * $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: n > N \implies \left\lvert{x_n - l}\right\rvert < \epsilon$

where $\left\vert{x}\right\vert$ is the absolute value of $x$.

Note
The definition of convergence of a sequence of Rational numbers is equivalent to the definition of convergence of a real sequence.