Computable analysis

In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis.

Computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers or the computable reals.

A function ${\displaystyle f\colon \mathbb {R} \to \mathbb {R} }$ is sequentially computable if, for every computable sequence ${\displaystyle \{x_{i}\}_{i=1}^{\infty }}$ of real numbers, the sequence ${\displaystyle \{f(x_{i})\}_{i=1}^{\infty }}$ is also computable.

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