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

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 .