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We combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider 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… (More)

We generalize the traditional concept of team learning. The success of an asymmetric team in learning some function depends upon the successes of participant machines by an arbitrary nondecreasing Boolean function. Asym-metric team types are ordered accordingly to their learning power by basic reductions. The problem to determine this order for an arbitrary… (More)

A FIN-learning machine M receives successive values of the function f it is learning and at some moment outputs a conjecture which should be a correct index of f. FIN learning has two extensions: (1) If M ips fair coins and learns a function with certain probability p, we have FINp-learning. (2) When n machines simultaneously try to learn the same function… (More)

In this paper we investigate in which cases unions of identiÿable classes are also necessarily identiÿable. We consider identiÿcation in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identiÿcation types still have features resembling closedness. For each of them we ÿnd n such that (1) if every union of n −… (More)