A construção dos números reais desenvolvida por Richard Dedekind

Abstract

In this work, we will study the emergence of incommensurability during classical antiquity and understand how this discovery was important for the development of real number theory during the arithmetic movement of analysis. Furthermore, our main focus will be on Richard Dedekind real number theory, studying and understanding the concept of “cuts” developed by him. Finally, we will briefly study, in a summarized way, the theory of Weierstrass and Cantor-Heine.