La Emancipaci\'on Conceptual de N\'umero Real de la Idea de Magnitud: Una Mirada Germ\'anica

TL;DR

This paper examines how three German mathematicians contributed to the conceptual separation of real numbers from physical magnitudes and highlights the role of arithmetization in the axiomatization of real numbers.

Contribution

It analyzes the historical contributions of three German mathematicians to the conceptual development and axiomatization of real numbers in the 19th century.

Findings

Identifies key contributions of German mathematicians to real number theory.

Highlights the importance of arithmetization in the axiomatization process.

Shows the shift from physical to abstract concept of magnitude.

Abstract

In the present article we study the decisive contributions of three members of the German mathematical school to the separation of the concept of number from the physical concept of magnitude, during the second half of the XIXth century. Besides we analyze the importance of the arithmetization of analysis to later axiomatization of real numbers, process that those three mathematicians promoted in the principal works we review.