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.

Sources

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