The Notion of Limit in 19th-Century Spanish Secondary Education Textbooks

Abstract

The process of formalization and arithmetization of the notion of limit took place essentially during the 19th century. During that period, the mathematical activity in Spain was very much oriented towards the production of textbooks. In this paper, we study the presence of this notion in the secondary education textbooks used in Spain during the 19th century, and we identify the different intuitive and formal phenomena that appear in them. We carried out documentary research of an exploratory and descriptive character, following the historical method. From the exhaustive analysis of 27 works, we see a clear tendency to include the limit mainly in works dedicated to algebra and arithmetic, frequently linked to successions, and using verbal representation. Among the phenomena organized on the basis of the different limits, those with a formal approach prevail.