On subrecursive representability of irrational numbers, part II

Article type: Research Article

Authors: Kristiansen, Lars^{; *}

Affiliations: Departments of Mathematics and Informatics, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway. [email protected]

Correspondence: [*] Corresponding author. [email protected].

Abstract: We consider various ways to represent irrational numbers by subrecursive functions. An irrational number can be represented by its base-b expansion; by its base-b sum approximation from below; and by its base-b sum approximation from above. Let S be a class of subrecursive functions, e.g., the class the primitive recursive functions. The set of irrational numbers that can be obtained by functions from S depends on the representation and the base b. We compare the sets obtained by different representations and bases. We also discuss how representations by base-b expansions and sum approximations relate to representations by Cauchy sequences and Dedekind cuts.

Keywords: Computable analysis, subrecursive functions, honest functions, irrational numbers

DOI: 10.3233/COM-170081

Journal: Computability, vol. 8, no. 1, pp. 43-65, 2019