Résumé
Functional equations are mathematical objects that are defined within the framework of algebra of functions (i.e. equation involving only the four arithmetical operations) for which the establishment of solutions most often requires recourses to methods of proof and proving specific to analysis. In this paper, we focus on the first Cauchy functional equation f(x + y) = f(x) + f(y) to highlight the role of order in such process, and to argue that the study of such functional equations is an effective means of simultaneously developing proof and proving skills and an understanding of the concepts involved when working with ordered sets of numbers, at university.s