La finestra del sindaco

This text is recommended to teachers and parents. Teaching and learning of limits (in Calculus) call for a deep research based on didactic, epistemological and mathematical contents. The so called epsilon-delta definition of limit for functions (and the analogous for sequences) is a knowledge obstacle so hard that in many countries curricula it recently disappears from high schools. We suggest didactic ways and tools for the learners' appropriation of this difficult concept with an analysis of the hidden mathematical tools involved in it, with suitable problems ad exercises.