An Historical Investigation about the Dedekind´s Cuts: Some Implications for the Teaching of Mathematics in Brazil

Francisco Regis Vieira Alves,Marlene Alves Dias

doi:10.24193/adn.11.3-4.2

Abstract

An Historical Investigation about the Dedekind´s Cuts: Some Implications for the Teaching of Mathematics in Brazil

Highlights

The definition of a solid basis for the foundation of the primitive concepts of Mathematical Analysis did not occur in a progressive, unstoppable or linear way (Alves, 2018a)
Given the existence of other mathematical forms and analytical methods employed for the formal establishment of a primitive notion for the theory of functions in a real variable, the notion of Dedekind's cut provides an indelible chapter in the History of Mathematics which, despite intuitive and heuristic ideas indicated by Richard Dedekind, the notion of cut, produced either by a rational number or by a non-rational number, finds its roots in ancient Greek thought
In the predecessor sections we address some elements that contribute to the understanding of a historical, mathematical, and evolutionary epistemological process about the notion of real number, whose construction here was accentuated as a contribution by Richard Dedekind, despite the existence of several mathematical methods and strategies for obtain it

Summary

Introduction

The definition of a solid basis for the foundation of the primitive concepts of Mathematical Analysis did not occur in a progressive, unstoppable or linear way (Alves, 2018a). In the present work we present some elements capable of providing an understanding on the evolutionary, historical and epistemological process of formalization of the notion of real number, especially from the thought of Richard Dedekind (1831 – 1916). Corry (2004) describes some of his academic background Dedekind studied in his native city of Braunschweig and in Göttingen. The decisive influence of the leading mathematicians of the early Göttingen tradition marked Dedekind's formative years. This influence was clearly manifest in all of his later work. In the subsequent section, we will point out some mathematical properties that were required by Dedekind aiming at the construction of real numbers

Some primitive properties

A Brazilian historical research proposal and the Mathematics teacher

Conclusion