Affiliation:
1. Rutgers University, Department of Mathematics, College of Arts and Sciences, New Brunswick, New Jersey
Abstract
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 respects.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference20 articles.
1. On the theorem of Cauchy in constructive analysis;CEITIN G. S;Usp. Mat. Nattc,1955
2. Review of llekursive reele Zahien 101;SEL G;Math. Revs.,1957
Cited by
23 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献