God created natural numbers, mathematicians did the rest. But what about professors? Consequences of the arithmetization of analysis in university texts.

Abstract

This paper analyzes the process of Arithmeticization of Mathematical Analysis and explores the consequences that this movement, culminated in the 19th century, had on the development of the concepts of function and real number in university textbooks and lecture notes of Analysis subjects at the National University of the Northwest in the province of Buenos Aires. It is concluded that this process of foundation left a significant mark regarding the definition of function, showing a tendency of authors towards modern and formal definitions. However, this influence is not observed in the same way in the definition of real number. The influence of the use of History in the development of concepts by authors of mathematical texts is also analyzed, where, on one hand, a uniform distribution is observed in terms of its frequency of use, and on the other hand, it is noted that in general, books do not respect the chronological order in which formalizations arose.