During their school life, students learn mathematical topics that can be considered essential for the understanding of the property of density in the set of real numbers. Therefore, we detected a need to design and elaborate a Hypothetical Learning Path to include topics to help promote the learning of this property. This report shows results of a first stage of an educational experiment as part of an ongoing research. It describes how through the trajectory, high school students are able to recognize ways of finding numbers in an interval using various semiotic representations. We also describe some difficulties that students had to recognize the non-existence of a successor in real numbers. [For the complete proceedings, see ED630060.]