Les extensions intrinseques les plus simples des ensembles R et N pour une nouvelle Analyse Non standard

The main results of this paper are the formal constructions, both rigorous and intuitive of the “Aleph” intrinsic extension of the set of non negative integers N and the “Omega” smallest strict over-field of R which is totally ordered and complete. The first differential and integral elements of a new Non Standard Analysis (NSA*) are given. This very simple NSA* is compared to A.Robinson’s and J.H.Conway’s.