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The main results of this paper are the formal constructions, both rigorousand intuitive of the "Aleph" intrinsic extension of the set of non negativeintegers N and the "Omega" smallest strict over-field of R which is totallyordered and complete. The first differential and integral elements of a new NonStandard Analysis (NSA*) are given. This very simple NSA* is compared toA.Robinson's and J.H.Conway's.

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