The purpose of this study was to investigate how a set of physical and digital instructional activities can serve as an example space to help further develop a concept image that is aligned with the formal concept definition for the limit of a sequence. In addition, the unique affordances and constraints allowed by using either a physical or digital modality in understanding the convergence of a sequence was analyzed. Results suggest that both of these activities served to help students conceptualize the arbitrary nature of the error bound, and for some students it further illustrated the relationship between an arbitrarily small error bound, the limit value, and the index of the sequence. The physical activity constrained students to think of the sequence as a finite terminating set of numbers whereas the digital activity provided additional information that student used in subsequent problem solving. [For the complete proceedings, see ED583608.]