Definition:Computable Real Sequence

Definition
Let $\sequence {x_n}$ be a real sequence.

Suppose that there exists a total recursive function $f : \N^2 \to \N$ such that:
 * For every $m, n \in \N$, $\map f {m, n}$ codes an integer $k$ such that:
 * $\dfrac {k - 1} {n + 1} < x_m < \dfrac {k + 1} {n + 1}$

Then $\sequence {x_n}$ is a computable real sequence.