Nonstandard analysis: New way and criticism of the previous approaches
Saghe, Abdeljalil
HAL, hal-01516131 / Harvested from HAL
Text on HAL
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 a few applications of the new approach, and we propose to compare it with the previous methods.
Publié le : 2017-04-28
Classification:  Keyword Nonstadard analysis,  hyppereals,  Internal set theory,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM],  [MATH]Mathematics [math] 
@article{hal-01516131,
     author = {Saghe, Abdeljalil},
     title = {Nonstandard analysis: New way and criticism of the previous approaches},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01516131}
}

Saghe, Abdeljalil. Nonstandard analysis: New way and criticism of the previous approaches. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01516131/