After reading a few articles about the rational points that could be found in the well-known Cantor set, I wondered if I could similarly find rational points in generalized Cantor sets too. Many years ago, I worked with a student to see what we could find. In this talk, I will briefly describe the Cantor set and the motivation for this project. After that I will discuss two different types of generalizations of the Cantor set and how to think about finding what lies inside of these sets.