# Analysis in the Computable Number Field

@article{Aberth1968AnalysisIT, title={Analysis in the Computable Number Field}, author={Oliver 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…

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