Differential calculus on IF sets

Abstract

This contribution summarizes the theory of differential calculus on IF sets. First the definition of the function is given. Then the absolute value and limit of the function are defined and the properties of these functions are studied. By using the limit of the function the derivative of the function is define and Lagrange mean value theorem is proved. Since the main aim of this contribution is to proof the Taylor’s theorem the polynomial function and Taylor polynomial are defined. Finally the Taylor’s theorem is proved and some examples are given.