In this report we show an investigation of how high-school students learn strategies to find intermediate numbers in an interval to understand the property of numerical density. Research has shown that some high-school students have difficulty in understanding this property. To mitigate this difficulty, we proposed a Hypothetical Learning Trajectory, using school mathematics topics, for high-school students to learn about numerical density. Our study showed that some students recognized that there is an infinite quantity of intermediate numbers in an interval; however, all the participants had difficulty understanding why there is no successor in a set other than the natural or integer numbers. [For the complete proceedings, see ED657822.]