Real Numbers and Computational Challenges Under a Phenomenological Perspective

Abstract

In this chapter we will examine the production of mathematical knowledge about real numbers and the challenges faced with the advent of digital technology under a phenomenological perspective. We understand that knowledge is produced through a process of subjectivity and intersubjectivity, which takes place in a community, by subjects who are in the world, and in a specific context. Therefore, all production needs to be considered in its social, historical, cultural, and temporal dimensions. Whereas at the time of the formalization of the concept of real numbers, it was not possible to think about the virtuality and logic that are in the construction of computers; the increasing significance of computers in the production of mathematics led us to inquire how to understand real numbers in their computational representation, and the challenges resulting from this process. In order to do this, we present the movement to formalize the concept of real numbers made in the nineteenth century, and the way they are computationally represented. In addition, throughout the chapter, we point out the challenges that emerged as we sought, as mathematical educators, to philosophically understand the approximations and divergences between Western mathematical sciences and mathematics performed by being with the computer.