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 of students successfully reinvented a definition of limit capturing the intended meaning of the conventional ?-? definition. This book traces the evolution of the students’ definitions over the course of two ten-week teaching experiments, and highlights thematic findings which point to what might be entailed in coming to reason flexibly and coherently about limit and its formal definition. This book should be especially useful for mathematics educators at the secondary and tertiary levels, particularly those who teach calculus and introductory analysis.

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