Definitional ambiguity: a case of continuous function

Definitions are an integral aspect of mathematics. In particular, they form the backbone of deductive reasoning and facilitate precision in mathematical communication. However, when an agreed-upon definition is not established, its ability to serve these purposes can be called into question. While ambiguity can be productive, the existence of multiple non-equivalent definitions for the same term can make the truth value of certain mathematical statements unclear. In this study, we asked mathematics educators to determine the truth of a definitionally ambiguous mathematical claim. Based on their responses, we identified several factors that influenced the teachers’ choice of definitions. Finally, we consider the pedagogical implications of employing such a task in teacher preparation programs