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 $k$ such that:

$\dfrac {k - 1} {n + 1} < x < \dfrac {k + 1} {n + 1}$

Then $x$ is a computable real number.

Sources

• This article incorporates material from computable number on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.