Internal set theory approach to nonstandard analysis
Abstract
Although epsilon-delta analysis has enjoyed great success in giving rigor to modern mathematics, nonstandard analysis can be used to rigorously reformulate modern arguments with infinite and infinitesimal arguments. The internal set theory approach to nonstandard analysis is an axiomatic approach that gives us a fresh point of view to look at mathematics. Together, nonstandard analysis with the internal set theory approach allows us to give novel proofs for classically difficult results.