nonstandard methods

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals, " which are numbers that are less than 1/2, 1/3, 1/4, 1/5, ..., but greater than 0. Abraham Robinson developed nonstandard analysis in the 1960s. The theory has since been investigated for its own sake and has been applied in areas such as Banach spaces, differential equations, probability theory, mathematical economics, and mathematical physics.

Ax-Kochen isomorphism theorem | hyperfinite set | logic | Łoś' theorem | model theory | superstructure | transfer principle | ultrapower | ultraproduct