Are all denumerable sets of numbers order-isomorphic?

Laura Branchetti (1) , Viviane Durand-Guerrier (2)

1 Department of Mathematics and Computer Science [Parma]
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: 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

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Laura Branchetti, Viviane Durand-Guerrier. Are all denumerable sets of numbers order-isomorphic?. INDRUM 2018, INDRUM Network, University of Agder, Apr 2018, Kristiansand, Norway. pp.14-23. ⟨hal-01849536⟩