1962/05/01 by Tibor Radó · 2 citations
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Computable function #Constructive #Mathematics #Diagonal #Enumeration #Set (abstract data type) #Function (biology) #Constant (computer programming) #Process (computing) #Pure mathematics #Discrete mathematics #Algebra over a field #Computer science #Geometry
paper · doi:10.1002/j.1538-7305.1962.tb00480.x
openalex publication_date 1962/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14
The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of non-negative integers has a largest element. Also, this principle is used only for sets which are exceptionally well-defined by current standards. No enumeration of computable functions is used, and in this sense the diagonal process is not employed. Thus, it appears that an apparently self-evident principle, of constant use in every area of mathematics, yields non-constructive entities.