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- W4313376020 abstract "The main goal of this chapter is to underline from an epistemological point of view the relevance of engaging university students in intertwined proving and defining practices. The chosen examples are real numbers and infinity, both concepts for which didactic research is still needed. In the first part of the paper, we illustrate the intertwined practices of proving and defining in the case of the construction of irrational numbers by Dedekind (1872) and Cantor (1872), recalling that for both authors, the need for these constructions emerged from proving issues. Next, we present an example of a situation involving R-completeness versus Q-incompleteness that has the potential to foster students’ engagement in intertwined proving and defining practices. In the second part of the paper, we explore the intertwined relationships between practices of enumeration, the definition of infinite sets, and diagonal proofs that the set of rational numbers is denumerable while the set of irrational numbers is not. We finish by addressing didactic implications." @default.
- W4313376020 created "2023-01-06" @default.
- W4313376020 creator A5090642219 @default.
- W4313376020 date "2022-01-01" @default.
- W4313376020 modified "2023-09-25" @default.
- W4313376020 title "Proving and Defining in Mathematics Two Intertwined Mathematical Practices" @default.
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- W4313376020 doi "https://doi.org/10.1007/978-3-031-14175-1_11" @default.
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