Models with Invertible Infinitesimals

Abstract

We have seen in the Introduction that at least two different kinds of infinitesimals have appeared in the literature. On the one hand, there are the nilpotent, whose use in handling “infinitesimal” structures like jets, prolongations, connections, etc. has been extensively illustrated in the preceding two chapters. On the other hand, there are the invertible infinitesimals which, together with infinitely large integers, are used to analyze such notions as limits and convergence along the lines of Non-Standard Analysis, as exemplified by Robin-son’s book. Thus, these types of infinitesimals serve different (and complementary) purposes, and both should appear in a theory of infinitesimals that is worth its salt.