INFINITYCALCULUS.ORG

Our work on Non-Archimedean Analysis is centered on the development of Analysis concepts on totally ordered Non-Archimedean Fields, in particular those first described by Levi-Civita. Those structures have the advantage of being particularly small, and even treatable in computational environments, which is not the case for the structures of the field of Non-Standard Analysis. While in the latter discipline, there is a generally valid transfer principle that allows the transformation of known results of conventional analysis, here all relevant calculus theorems are developed separately, which is facilitated by theorems that under certain conditions allow the extension of classical behavior into infinitely small neighborhoods... Our work encompasses developing various calculus concepts including smoothness approaches that allow to formulate intermediate value theorems, theorems about ranges, and local expandability in Taylor series in various topologies. We have also developed..

Primary location: East Lansing United States