Here we use the evolving framework of structural abstraction as a theoretical lens to investigate how mathematics major university students understand the limit concept of a sequence. To this aim the theoretical framework is outlined and previous empirical data on one individual's partial (re-)construction of a convergent sequence is revisited. In doing so, we provide insights in how students who consider the formal definition of a mathematical concept as one of the components of their concept image involve it into their overall mathematical discourse when building new knowledge. Deeper analysis also reveals unsettled issues about structural abstraction and provides new directions for advancing our understanding of this kind of abstraction.