On subrecursive representability of irrational numbers

Article type: Research Article

Authors: Kristiansen, Lars^{a; b}

Affiliations: [a] Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo, Norway | [b] Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, NO-0316 Oslo, Norway. larsk@math.uio.no

Abstract: We consider various ways to represent irrational numbers by subrecursive functions: via Cauchy sequences, Dedekind cuts, trace functions, several variants of sum approximations and continued fractions. Let S be a class of subrecursive functions. The set of irrational numbers that can be obtained with functions from S depends on the representation. We compare the sets obtained by the different representations.

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

DOI: 10.3233/COM-160063

Journal: Computability, vol. 6, no. 3, pp. 249-276, 2017