Completitud y continuidad revisadas a través de 23 siglos: aportes a una investigación didáctica

We present in this paper an historic-epistemological analysis about the notion of real numbers set completness. In this analysis we connect problems and questions at determined historical periods with the state of knowledge and available tools at those times and also with the different produced conceptualisations. The relationship between numbers and magnitudes as well as the different stages of the notions about line continuity and numerical system completness are analyzed on the basis of specific historical data, which are presented in many cases with the original texts as support. The questions guiding this study arise from a didactic reflection. The kind of analysis performed allows us to state conclusions that would be useful for Education. This study is enclosed in a larger Math Education research about the concept of real numbers set.