Epistemological messages conveyed by three high-school and college mathematics textbooks

Mathematics textbooks embody a particular set of assumptions about mathematics or the mathematics intended for students at a particular level. Thus, an epistemological analysis of textbooks can provide some context for understanding, for example, the difficulties many students encounter when moving from high-school to collegiate mathematics. In this study, we consider how typical pre-calculus, calculus, and analysis texts treat the topic of continuity. We find that these texts send conflicting messages regarding the status and purpose of mathematical definitions.