An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close approximations of the subject's preference, even when the limiting (countably infinite) data are enough to infer the preference perfectly. We provide sufficient conditions on the set of alternatives, preferences, and sequences of pairs so that the observation of finitely many choices allows the experimenter to learn the subject's preference with arbitrary precision. While preferences can be identified under our sufficient conditions, we show that it is harder to identify utility functions. We illustrate our results with several examples, including consumer choice, expected utility, and preferences in the Anscombe-Aumann model.