Infinitesimal Calculus, Consistently and Accessibly

The most important feature of Nelson’s [60] radically elementary analysis is the discretization of the continuum. The crucial step herein is the consistent use of infinitely large (“nonstandard”) numbers and infinitesimals, in a manner which was first proposed by Nelson through the axiom system of Internal Set Theory [59], motivated by the groundbreaking work of Abraham Robinson [66, 67]. One decade on, Nelson [60] introduced an even more elementary, yet still very powerful, formal system, which we shall review presently.