Résumé
The relationship between truth in an interpretation and validity in a theory as developed in logic, is a crucial issue in mathematics. In this article, we examine how an activity based on the equality "1 = 0.999 ..." could permit students to experience this relationship. We first provide practical and epistemological reasons supporting the claim that we have here a good candidate for this purpose. We then report on an experiment with nine fresh undergraduate students in France enrolled as volunteer in a short course aiming to help them to overcome difficulties in logic, reasoning and proof met in the calculus course; we analyse some excerpts of students' discussion showing that questioning this equality could favour the emergence of discussion on truth, validity, defining and proving, proof and theoretical reference