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ERIC Number: EJ1012684
Record Type: Journal
Publication Date: 2013
Pages: 18
Abstractor: As Provided
Reference Count: 25
ISSN: ISSN-1051-1970
Convergence and the Cauchy Property of Sequences in the Setting of Actual Infinity
Shipman, Barbara A.
PRIMUS, v23 n5 p441-458 2013
Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and analysis. After characterizing this point of view, this paper reformulates the definitions of convergence and the Cauchy property in the setting of actual infinity. This yields a conceptually streamlined approach and simple proofs of classic results on sequences. The paper also presents pedagogical metaphors that guide students in defining limit and the Cauchy property from the actually infinite standpoint. (Contains 5 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A