ERIC Number: EJ985836
Record Type: Journal
Publication Date: 2012-Sep
Pages: 3
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0746-8342
EISSN: N/A
Series that Converge Absolutely but Don't Converge
Kantrowitz, Robert; Schramm, Michael
College Mathematics Journal, v43 n4 p331-333 Sep 2012
If a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false. We provide examples of rational series that illustrate this point. The Cantor set appears in connection with one of the examples.
Descriptors: Mathematics Instruction, College Mathematics, Mathematical Concepts, Validity, Mathematical Logic, Serial Ordering
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A