Notion de limite et décimalisation des nombres réels au lycée

The results of an epistemological investigation about the inter-relations historically built between the construction of real numbers, the notion of limit and the decimalisation of real numbers lead us to a description of Mathematical Organisations (OM), that we qualified as reference OM. From an institutional analysis (chronological evolution of curricula, instructions and textbooks) we identify mathematical organisations to be taught, interpreted as traces of reference OM in the teaching of mathematics. The distance between reference OM and OM to be taught are explained by conditions and constraints proper to each institution, lower and upper secondary mathematics education. Building, experimenting and analysing a didactical engineering is a means for us to give some elements of answer to the question of viability of a teaching aiming at introducing (under today¿s conditions and constraints) a topological viewpoint on the notion of limit in relation with the decimalisation of real numbers in a calculator environment.