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.
The overspill principle has a number of useful consequences: In particular: These facts can be used to prove the equivalence of the following two conditions for an internal hyperreal-valued function ƒ defined on *R. and The proof that the second fact implies the first uses overspill, since given a non-infinitesimal positive ε, Applying overspill, we obtain a positive appreciable δ with the requisite properties.
These equivalent conditions express the property known in nonstandard analysis as S-continuity (or microcontinuity) of ƒ at x. S-continuity is referred to as an external property.
The first definition is external because it involves quantification over standard values only.