PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Conversations on Density of Q in R
Page: 393
We explore the notion of density of the set of rational numbers in the set of real numbers, as interpreted by undergraduate mathematics students. Participants’ responses to a scripting task, in which characters argue about the existence of one or infinitely many rational numbers in a real number interval, comprise the data for our study. The framework of reducing abstraction is used in explaining the participants’ mathematical behavior when coping with the task. The analysis reveals informal ideas related to density as well as unconventional understandings of density-related concepts of rational numbers and infinity