Competency has been the buzzword of higher education for at least a decade. The reasonable approach of describing what students should be able to do after completing coursework, however, falls short of the fact that mathematics, like any subject matter, contains inherent difficulties for students. Students usually need assistance in overcoming such difficulties. Competency-driven approaches to the curriculum tend to ignore this issue. In this article, this problematic issue will be exemplified by investigating students' difficulties with the concept of the empty set on one hand and the framework of the European Society for Engineering Education (SEFI) for a mathematics curriculum on the other hand.