Discussions about the Relation between Limit and Continuity of a Function: investigating Concept Images

Abstract

This paper presents the results of an investigation that was made with university students enrolled in the 3^rd and 4^th semester of graduation in mathematics at two public universities in the state of Pará (Brazil). We aimed to investigate the concept image of these subjects about the relation between limit and continuity of a function, through an exploratory study done in two stages. The results were related to the researches of Tall and Vinner (1981), Vinner (1991) that composed our theoretical framework. Among the evoked concept images, we emphasize the idea that when a function is not defined in one point of the domain implies, necessarily, in the non-existence of the limit of that function in that point. That is, according to them, the limit's existence depends on the continuity of the function.

Keywords:
Concept Image; Limit of a Function; Continuity