In this study, it was aimed to determine both prospective teachers’ proving approaches related to equivalence of infinite sets and their difficulties about this subject. In accordance with this purpose, a form including open-ended questions was developed to collect data and it was applied to 121 mathematics teacher candidates. Obtained data were analyzed via content analysis. Proof scheme introduced by Blum and Kirsch (1991) was taken into account for categorizing proofs. Consequently, it was identified that prospective teachers can adopt both formal and pre-formal approaches in their proving activities. In addition, it has been seen that individuals, who used pre-formal approach, can use their formal knowledge and intuitions together in proving activities. On the other hand, misconceptions, lack of knowledge and methodological deficiencies, which caused to candidate teachers to fail constructing proof, were identified and especially the misconceptions of them were presented through separate headings.