Graphical definition of the limit of a function, contribution to its formality as geometric didactics

Abstract

The limit of a function is a concept rejected by students starting university studies, its current formal definition is an algebraic algorithm of topological notions with the famous: Delta and Epsilon, which are usually ignored in the teaching discourse, and even removed from the programs, considering that they are very abstract contents for the noble minds of the first university mathematicians. In fact, some research on teaching shows that these professionals do not know the Spanish definition of the limit and their education is centered on the formalism of its definition and on the resolution of some problems. In this article the formal definition is explained geometrically and analytically, where it is explained why several solutions occur, with unpublished development in transcendent functions. The work proposes new theorems and an academic proposal to the Mathematics I program.