Affiliations: Departments of Mathematics and Informatics, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway. firstname.lastname@example.org
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.