Students’ work with limits of functions includes the concept of infinity. These concepts, limits and infinity, are complex but necessary for mathematics studies. A study of student solutions of limit tasks was conducted to reveal how students handled limits of functions and infinity at a Swedish university (Juter, 2005). This led us to question about how pupils’ identities were formed in upper secondary school mathematics. In this study questions were raised about the background of the students’ and teachers’ situations concerning textbooks and curricula for upper secondary school. We have analysed examples from Swedish textbooks and curricula. The theoretical framework used builds on Tall and Vinner’s work (1981) on formal concept definition, personal concept definition and concept images. The lack of proper preparation opportunities for pupils about limit and infinity and the lack of connections between the way mathematics is presented in upper secondary school and at university level have consequences for the development of identity of the students. Teachers’ opportunities for differentiated exposition which may meet different student needs are limited by the ways textbooks are leaving out options to explore, in a more substantial way, the concepts of limits and infinity. Thus textbooks guide teachers’ mediation of mathematics for pupil learning in limited ways.