THE CONCEPT OF FINITE LIMIT OF A FUNCTION AT ONE POINT: STRUCTURAL ASPECTS AND PERSONAL DEFINITIONS

The purpose of this work consists of describe and interpret the personal definitions related to the concept of finite limit of a function at one point in terms of structural aspects, compiled and synthesized from prior research. These aspects are: the interpretation of the limit notion as an object or a process, its exact or approximate character, algorithms and practical skills for its calculation, its reachability and its possibility of being exceeded. On the base of these structural aspects, we analyze the personal definitions provided by a group of non-compulsory secondary education students on the concept of finite limit of a function at one point. Among results we point out the richness of meaning from these definitions, either by the not reachable and not exceedable character of the limit, and the dual consideration of the limit as an object or process.