Abstract
This article focuses on the real number in high school, and the way that teachers and students from high school and university interact with it. Through a case study carried out in the Montpellier Academy during the 2012-2013 school year, and extended into 2014, we tried to collect, from first and third year scientific sections highschool students, and university science students, their conceptions of the real numbers, and we compared each with the others. To this end, we have identified these conceptions through two questionnaires that we analised in the light of our epistemological study. Finally, we suggest some directions to start as soon as high school an approach of the real number concept.