Students’ perceptions of the completeness property of the set of real numbers

Abstract

This article presents an exploratory study that gives account of some students’ perceptions of the completeness property of the set of real numbers. Students taking three undergraduate correlative courses in Calculus and Analysis answered a written questionnaire; their scripts are analysed trying to understand how operational is the notion of completeness for them and to what extent they take this notion for granted.

Keywords:

• real numbers
• completeness
• university level
• students' perceptions

Notes

Notes

1. As one of the reviewers suggested, it might be more accurate to denote this type of answer as potentially operational rather than operational (if so, it would be actually operational for advanced students and mathematicians that do operate with the definition).

2. Jumps and lacunas are kinds of cuts. For instance, all cuts in the set of integer numbers are lacunas, all cuts in the set of rational numbers are jumps.