Foundations of Infinitesimal Calculus

Аннотация

The actual situation, as suggested by Leibniz and carried out by Robinson, is that one can form the hyperreal number system by adding infinitesimals to the real number system, and obtain a powerful new tool in analysis. The reason Robinson's discovery did not come sooner is that the axioms needed to describe the hyperreal numbers are of a kind which were unfamiliar to mathematicians until the mid-twentieth century. The method is surprisingly adaptable and has been applied to many areas of pure and applied mathematics. It is also used in such fields as economics and physics as a source of mathematical models. However, the method is still seen as controversial, and is unfamiliar to most mathematicians.