Are all denumerable sets of numbers order-isomorphic?

Laura Branchetti; Viviane Durand-Guerrier

Are all denumerable sets of numbers order-isomorphic?

Acte de colloque

Open Access

Are all denumerable sets of numbers order-isomorphic?

Laura Branchetti et Viviane Durand-Guerrier

Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018), pp.14-23

INDRUM 2018 (Kristiansand, Norway, 05/04/2018–07/04/2018)

Résumé

concept image versus definition

Epistemological studies of mathematical topics

Concept image and concept definition.

Teaching and learning of analysis and calculus

Density

denumerable set

Ordered set

In this paper we study cognitive conflicts on the issue of number sets being dense, ordered and denumerable. We first provide historical-epistemological background related to these notions. Then we consider the cognitive conflicts under the lenses of concept image and concept definition, which we use to analyse empirical data collected in order to understand better the didactical and cognitive issues at stake.

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Détails

Titre: Are all denumerable sets of numbers order-isomorphic?
Créateurs - sans rôle: Laura Branchetti - Department of Mathematics and Computer Science [Parma]
Viviane Durand-Guerrier - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Contributeurs - sans rôle: Viviane Durand-Guerrier
Reinhard Hochmuth
Simon Goodchild
Ninni Marie Hogstad
Détails de publication: Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018), pp.14-23
Colloque: INDRUM 2018 (Kristiansand, Norway, 05/04/2018–07/04/2018)
Identifiants: 9944344509311
Unité académique: Institut Montpelliérain Alexander Grothendieck - IMAG
Langue: English
Type de ressource: Conference proceeding
Champs locaux: hal-01849536