Burn (2005) proposes a "genetic approach" to teaching limits of numerical sequences. The article includes an explanation of the Method of Exhaustion, a generalization of this method, and a description of how this method was used for obtaining areas and lengths in the seventeenth century. The author uses these historical and mathematical analyses as a basis for proposing an alternative definition of the limit of a sequence. The paper focuses on the fine mathematical and historical detail of the notion of limit. Reading it made me reflect on the explicitly or implicitly involved didactical aspects, which I would like to share with "Educational Studies in Mathematics" readers.