Limit plays a vital role as a foundational concept in analysis. The vast majority of topics encountered in calculus and undergraduate analysis are built upon understanding the concept of limit and being able to work flexibly with its formal definition. This book describes a study conducted with the purpose of: 1) Developing insight into students' reasoning about limit in relation to their reinventing the formal definition, and; 2) Informing the design of principled instruction that might support students' attempts to reinvent the formal definition. In separate teaching experiments, two pairs...