Perhaps this question overlaps with similar ones, … but I want to focus on a particular possible cause of confusion. I notice that students are often confused by the concepts of "infinite" and "unbounded". So, when asked if the set of invertible matrices is compact, they reply "no, because there are an infinite number of matrices with non zero determinant, therefore the set is unbounded". Actually this happens in Italian, where the corresponding words ("infinito" and "illimitato") are almost synonyms in everyday language. Does this happen in English too, or other languages?. I wonder: what if we chose another name for the two concepts? Would they make this mistake anyway? One way to check this would be to compare with what happens in other languages, where perhaps the words chosen do not create the confusion. Do you have other examples of this situation? Can you suggest different math concepts which in one language are named with synonyms, but not in another? Do you know if this problem has been studied anywhere?
[Math] Do names given to math concepts have a role in common mistakes by students
soft-questionteaching
Related Question
- [Math] The average number of people that can sit on a bench of a given length.
- [Math] Does seeing beyond the course you teach matter? The case of linear algebra and matrices
- [Math] What non-categorical applications are there of homotopical algebra
- [Math] Amount of math research published in other languages
- [Math] Languages beyond enumerable
Best Answer
"Open" and "closed". Every reasonable human being on the planet, who has not studied topology, will assume that something can either be open or closed, but not both. This often causes students to make statements like "Set A is open, therefore it is not closed, thus ..."