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Completeness of Ordered Fields and a Trio of Classical Series Tests
Joint Authors
Kantrowitz, Robert
Neumann, Michael M.
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-06
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field.
It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, none of the three is valid in any proper subfield of R.
The argument hinges on a contractive-type property for sequences in Archimedean ordered fields that are bounded and strictly increasing.
For an arbitrary ordered field, it turns out that each of the tests of Dirichlet and Dedekind is equivalent to the sequential completeness of the field.
American Psychological Association (APA)
Kantrowitz, Robert& Neumann, Michael M.. 2016. Completeness of Ordered Fields and a Trio of Classical Series Tests. Abstract and Applied Analysis،Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1094760
Modern Language Association (MLA)
Kantrowitz, Robert& Neumann, Michael M.. Completeness of Ordered Fields and a Trio of Classical Series Tests. Abstract and Applied Analysis No. 2016 (2016), pp.1-6.
https://search.emarefa.net/detail/BIM-1094760
American Medical Association (AMA)
Kantrowitz, Robert& Neumann, Michael M.. Completeness of Ordered Fields and a Trio of Classical Series Tests. Abstract and Applied Analysis. 2016. Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1094760
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1094760