The system of integer functions, an efficient version of discrete mathematical analysis

Abstract: The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer functions intends to help to make the transition from the present approach to the problems of the calculus to a more computer-centric one as smooth and efficient as possible , and to find a way to some kind of synthesis of the discrete and continuous .