Finding and proving supremum and infimum: Students' misconceptions

Abstract

The real numbers system is one of the topics that pre-service mathematics teachers have to master. There is no exception to supremum and infimum, the basic concept of completeness properties of the real numbers system. They face with these two concepts in the second year and they require these two concepts all their undergraduate-study long. This paper focuses on analyzing pre-service mathematics teachers' misconceptions on finding and proving supremum and infimum of a set of the real number system. The study reported in this paper was done by qualitative research. A test was given to 62 students who took Introduction of Real Analysis. Numerous misconceptions found between supremum and upper bound, not to mention infimum and lower bound. The misconception about the definition of supremum and infimum, the theorem of supremum and infimum, and the basic concept of mathematics were described as well.