Exemplar-based learning is a theory in which learning is accomplished by storing points in Euclidean n-space, En. This paper presents a new theory in which these points are generalized to become hyper-rectangles. These hyper-rectangles, in turn, may be nested to arbitrary depth inside one another. This representation scheme is sharply different from the usual inductive learning paradigms, which learn by replacing boolean formulae by more general formulae, or by creating decision trees. The theory is described and then compared to other inductive learning theories. An implementation, Each, has been tested empirically on three different domains: predicting the recurrence of breast cancer, classifying iris flowers, and predicting survival times for heart attack patients. In each case, the results are compared to published results using the same data sets and different machine learning algorithms. Each performs as well as or better than other algorithms on all of the data sets.