Completeness of Ordered Fields and a Trio of Classical Series Tests
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 a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/6023273 |