Abstract
In this article, we identify logical contradictions between two different approaches to the notions of limit and continuity of a real function: that of Calculus books and the one usually found in Real Analysis books. In addition to pointing out these contradictions, we indicate their origin and briefly comment on possible consequences for teaching and learning university mathematics, especially in courses which have Real Analysis as a mandatory part of their curricula. The negative impact of these contradictions on students’ learning may demand a particular concern in Mathematics undergraduate courses, where Real Analysis comes after a two-year teaching/learning process that crystallizes the Calculus books approach. The way it was conceived, this study might also contribute to the professional development of mathematics teacher educators and Calculus teachers in general.
University Mathematics Education; Differential and Integral Calculus; Real Analysis; Limit and Continuity of Real Functions; Logical Contradictions