Modifying and extending Cantor set for better understanding of the concept of limit

Abstract

When dealing with Calculus, one of the most important and delicate ideas is the idea of limit. On one hand, in the beginning, when it is taught, it is not easy to grasp it. On the other hand, when it seems to have become rather easy to use it, one then must be very careful because it may also become easy to get wrong results. This paper uses and extends the Cantor set ideas and attempts to use it in order to facilitate better understanding of such fine concepts as function limit, derivative, and derivative limit.