Creating subsets of rational numbers in Mathematica for graphing purposes poses challenges due to the density of rational numbers in any interval, such as [0, 1]. The discussion highlights the difficulty in graphing a set of rational numbers since they are dense, meaning that between any two rational numbers, there are infinitely many others. While the idea of graphing a segment with "holes" for irrational numbers was considered, it was concluded that this cannot be accurately represented in a traditional graphing sense. A workaround was found using a tablet and OneNote to visually illustrate the concept with open circles, but no direct solution in Mathematica was identified for this specific graphing task.