On the inductive inference of recursive real-valued functions

We combine traditional studies of inductive inference and classical continu ous mathematics to produce a study of learning real-valued functions. We co nsider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbit rary computable functions of recursive real numbers. In each case we find n atural examples of learnable classes of functions and unlearnable classes o f functions. (C) 1999 Elsevier Science B.V. All rights reserved.