%0 Journal Article %T Des nombres infiniment petits et des entiers infiniment grands mais d¨¦finis ¨¤ l'unit¨¦ pr¨¨s %A Bautier Thierry %J Mathematics %D 2011 %I arXiv %X The main results of this paper are the construction, both rigourous and intuitive, of "the" intrinsic extension of the set of non negative integers N and the smallest over-field of R set which is continue (according to R.Dedekind). The aim of this article is to provide a new Non Standard Analysis, very simple, which is compared in the Introduction with A.Robinson's and J.H.Conway's %U http://arxiv.org/abs/1103.1655v1