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Communication Dans Un Congrès Année : 2022

On the dialectical relationship between truth and proof: Bolzano, Cauchy and the intermediate value theorem

Viviane Durand-Guerrier

Résumé

The question of the nature of the relationship between truth in an interpretation and proof in a mathematical theory is a complex epistemological issue. From a didactic perspective, we argue that it is worthwhile to address this issue in mathematics teaching and learning. In this paper, we illustrate this in the context of the Intermediate Value Theorem, focusing on the approaches of Bolzano and Cauchy, and we discuss possible didactic implications.
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Dates et versions

hal-03746871 , version 1 (06-08-2022)
hal-03746871 , version 2 (17-10-2022)

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  • HAL Id : hal-03746871 , version 2

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Viviane Durand-Guerrier. On the dialectical relationship between truth and proof: Bolzano, Cauchy and the intermediate value theorem. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, Bozen-Bolzano, Italy. ⟨hal-03746871v2⟩
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