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About: Overspill     Goto   Sponge   NotDistinct   Permalink

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In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers. By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction: For any internal subset A of *N, if 1. * 1 is an element of A, and 2. * for every element n of A, n + 1 also belongs to A, then A = *N In particular: