Saghe Abdeljalil - Cpge de Settat, Lycee Qualifiant Technique PB: ۵۷۶-Maroc.

In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing  a few applications of this approach with the former methods.

Nonstandard analysis, Hyppereals, Internal set theory