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Communication Dans Un Congrès Année : 2013

0, 999... = 1: An equality questioning the relationships between truth and validity

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
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Dates et versions

hal-00821767 , version 1 (13-05-2013)

Identifiants

  • HAL Id : hal-00821767 , version 1

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Judith Njomgang-Ngansop, Viviane Durand-Guerrier. 0, 999... = 1: An equality questioning the relationships between truth and validity. Eighth Congress of the European Society for Research in Mathematics Education, Feb 2013, Antalya, Turkey. A paraître en 2013. ⟨hal-00821767⟩
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