L'utilisation des quantificateurs universel et existentiel en première année d'université, entre l'explicite et l'implicite

In the first part of our paper, we present some epistemological and didactical aspects of the concept of quantification that show the complexity of quantifiers in both formal and natural language. In the second part, we present a logical formalization of the objects and structures that occur in the definition of a distinct object taught at university: the concept of upper limit. The didactic analysis of textbooks and course notes concerning upper limit, as well as an interview with pairs of students in a problem-solving situation, revealed, on the one hand, the didactic phenomena related to the alternation of the two types of quantifiers and, on the other hand, difficulties in mobilizing the definition of the objects and the structures, which illustrate a major problem in the conceptualization process.