Zone of Concept Image Differences in Infinite Limits at Undergraduate Level

The gap between the concept image and the concept definition will greatly affect a person’s understanding of the concept. This study aims to reveal the gap between the concept image and the concept definition, and the causes of the emergence of the gap. The research subjects were 16 first-year mathematics students at one of the universities in Aceh, Indonesia. Data were obtained from the results of written tests and in-depth interviews. This qualitative research with a phenomenological study approach was analyzed descriptively. The results showed that the gap that occurs in the concept includes: the division of a non-zero number by zero yields infinity, the concept of dividing zero by zero is zero, the concept of dividing a number by zero is the same as the concept of the limit, e.g., , and the concept of the left-hand limit as means that the satisfied value of x is all negative numbers such that . The emergence of these concept images results from the subject's learning experience at school and a calculus course. This finding provides insights and considerations for educators to comprehensively introduce students to the concept of infinity to avoid misunderstandings in limit and next materials