1968/04/01 by Oliver Aberth · 1 citation
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Bounded function #Combinatorics #Computability, Logic, AI Algorithms #Computable analysis #Computable function #Computable number #Computer science #Constructive #Countable set #Discrete mathematics #Field (mathematics) #Limit (mathematics) #Logic, programming, and type systems #Mathematical analysis #Mathematics #Monotone polygon #Pure mathematics #Real analysis #Real number #Sequence (biology) #Set (abstract data type)
paper · pdf · doi:10.1145/321450.321460
openalex publication_date 1968/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
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.