### Abstract

This study explored students' understanding of a logical structure in defining the limit of a sequence, focusing on the relationship between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience with rigorous proofs using the ε-N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε-N definition. By analyzing the students' responses to the validity of the statements as definitions of the limit of a sequence, students' understanding of such a relationship was classified into five major categories. This paper discusses some essential components that students must conceptualize in order properly to understand the relationship between ε and N in defining the limit of a sequence.

Original language | English (US) |
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Pages (from-to) | 263-279 |

Number of pages | 17 |

Journal | Educational Studies in Mathematics |

Volume | 73 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2010 |

### Keywords

- Error bound
- Limit
- Logical structure
- Relationship between ε and N
- Sequence
- ε-N definition
- ε-strip activity
- ε-strip definition

### ASJC Scopus subject areas

- Mathematics(all)
- Education