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

TL;DR

This paper introduces a new system of integer functions that is independent of traditional analysis but aims to facilitate a smooth transition to computer-centric calculus and synthesize discrete and continuous mathematics.

Contribution

It proposes a fully independent system of integer functions that bridges discrete and continuous analysis, enhancing computational approaches in calculus.

Findings

Establishes a mutual correspondence between integer functions and real functions.

Provides a framework for transitioning from classical to computer-centric calculus.

Aims to synthesize discrete and continuous 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 .