A study of pre-service primary school teachers' content knowledge regarding real numbers related to infinity, i.e., division by zero and denseness of the real number line, was conducted at a Swedish university. Data were collected twice during the respondents' teacher education using questionnaires and interviews on both occasions. The data were analysed in terms of traces of concept images, focusing on general and specific arguments in different mathematics contexts. The results show that the pre-service teachers often used conflicting general and specific arguments to explain the same phenomena. Some concrete arguments used for explanations represented other mathematical structures than the ones intended. The results raise questions of the pre-service teachers' awareness of their own capabilities. Implications teacher education programmes are discussed.