The ring of fluxions
  The ring of fluxions (real sequential germs at infinity) provides a rigorous approach to infinitesimals, different from the better-known approach of Abraham Robinson. The basic idea was first espoused in a paper by Curt Schmieden and Detlof Laugwitz published in 1958. Although this ring codifies all the usual intuitive properties of infinitesimals in a very elementary way, its existence has been generally ignored. 
S.R. Doty
math.FA