Discrete Euclidian Spaces: a starting point toward the discretization of mathematics

TL;DR

This paper introduces Discrete Euclidian Spaces as foundational structures for discretizing mathematics, highlighting their impact on redefining core concepts like numbers and numeration systems.

Contribution

It presents a new framework called Isodimensional Discrete Mathematics that redefines mathematical foundations through discretization, offering a novel perspective on traditional concepts.

Findings

IDM roots in DESs influence mathematical foundations

Discretization offers alternative definitions of numbers and systems

Potential for significant theoretical impact on traditional mathematics

Abstract

Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is currently independent of Euclidean spaces -have in the Isodimensional Discrete Mathematics (IDM) their roots in the DESs. This mathematics, which arises largely from the discretization of traditional mathematics, presents its foundations and concepts differently from the orthodox way, so at first glance it may seem that the IDM could be an exotic tool, or perhaps just "a simple curiosity." However, the IDM dis-crete approaches have a great theoretical repercussion on traditional mathematics.