On Subrecursive Representability of Irrational Numbers, Part II

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 relates to representations by Cauchy sequences and Dedekind cuts.