Definition:Sequentially Computable Real Function

Definition

Let $f : \R \to \R$ be a real function.

Suppose that, for every computable real sequence $\sequence {x_n}$:

The real sequence $\sequence {\map f {x_n} }$ is also computable.

Then $f$ is a sequentially computable real function.

Sources

• 1957: A. Grzegorczyk: On the definitions of computable real continuous functions (Fund. Math. Vol. 44, no. 1: pp. 61 – 71)

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