In a course emphasizing interactive technology, 19 students, including 18 mathematics education majors, mostly in their first year, reinvented the definition of limit of a sequence while working in small cooperative groups. The class spent four sessions of 75 minutes each on a cyclical process of guided reinvention of the definition of limit of a sequence for a particular value, L = 5. Tentative definitions were tested systematically against a well-chosen set of examples of sequences that converged, or not, to 5. Students shared their definitions and the problems they were having with their definitions with their peers through whole class presentations and public postings on a course electronic forum. Student presenters received feedback from their peers both in person and through the forum. The approximation, error, error bound framework was used to help structure students' thinking. The use of interactive examples with epsilon bands and movable N values, in which students could zoom in to adjust the value of epsilon or zoom out to find a value of N, proved especially helpful in the process. The changes in their tentative definitions show the difficulties students had as well as the learning that occurred.