PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
The effects of the epsilon-N relationship on convergence of functions
Page: 236
Much work has been done in recent years to study students’ formulations of formal limiting processes. One of the most common goals is to foster a productive understanding of the relationship between the error bound epsilon and the domain of the convergence; what is called a range-first perspective. My study examines an advanced calculus student’s understanding of the relationships involved in convergence of functions, and how his prior experience with limits influenced his understanding. I unpack his cognitive organization of the dependence relationships between epsilon, N , and x in functional convergence. This case study demonstrates the effects of a persistent understanding that epsilon depend on N in the convergence of sequences.