# Students’ images and their understanding of definitions of the limit of a sequence

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## Abstract

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students’ images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the *ɛ*–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.

## Keywords

Asymptotes Cluster points Images Limits Rigorous definitions Sequences## Notes

### Acknowledgement

The author thanks Professor Sigrid Wagner, Professor Alfinio Flores, and three anonymous reviewers for their helpful comments on earlier versions of the article.

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