Definition:Computable Real Number

Definition
Let $x \in \R$ be a real number.

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

Then $x$ is a computable real number.