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Abstract
This paper has two integrated parts. In the first part, a task is introduced around the concept of equivalence relation. The initial aim of the task is to lead undergraduate students to define an equivalence relation as traditionally defined. The task is tried out on a small sample of students. Based on students' experience of the situation I reveal a change in my perspective in which I learned to consider defining in the realm of organising. The results of this change are reported in the second part of this paper in which I report a certain way of organising the given situation, a 'new' definition of equivalence relations, and consequently a new representation for them, that seems to be overlooked in the literature.