TY - JOUR ID - 34187 TI - A New Approach to Nonstandard Analysis JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Abdeljalil, Saghe AD - Cpge de Settat, Lycee Qualifiant Technique PB: 576-Maroc. Y1 - 2018 PY - 2018 VL - 12 IS - 1 SP - 195 EP - 254 KW - Nonstandard analysis KW - Hyppereals KW - Internal set theory DO - 10.22130/scma.2018.63978.244 N2 - 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. UR - https://scma.maragheh.ac.ir/article_34187.html L1 - https://scma.maragheh.ac.ir/article_34187_1dc006e0051c51f4fe5705b57c2673a0.pdf ER -