@article{Aberth1968AnalysisIT,
title={Analysis in the Computable Number Field},
author={O. Aberth},
journal={J. ACM},
year={1968},
volume={15},
pages={275-299}
}

It is well known that real variable analysis is nonconstructive. For example, although it is asserted that every bounded monotone sequence converges to a limit, there is no algorithm for obtaining this limit.
This paper presents a constructive analysis which is restricted to a countable set of numbers, the field of computable numbers. These numbers are defined in a new way by employing the concept of “programmable functions.” The resultant analysis differs from real analysis in many important… CONTINUE READING