Topological Essence of the Concept “Limit of a Numerical Sequence” in the General Mathematics

Abstract

High school mathematics includes a number of extremely important concepts, including the concept of the limit of the number sequence. However, most students when learning it do not understand it with certainty, but only accept it to apply it to solve exercises. This paper aims to give a topological essence of the concept of limit of a sequence and present some methods for teaching this concept in general school in Viet Nam. The Paper consists of four parts. Part 1 presents an introduction to the definition of “Limit of a sequence”, part 2 deals with Some properties derived from definitions and notes in teaching, part 3 covers the Mathematical essence of the concept limit of a number sequence and part 4 talks about Defining topology on the set of real numbers. In each section, we include comments to help teach these notions and concepts. In each section, we make comments and observations to teach these concepts better.