Kantrowitz ’82 Publishes Article on Ordered Fields
An article titled “Completeness of Ordered Fields and a Trio of Classical Series Tests” co-authored by Professor of Mathematics Robert Kantrowitz ’82 appears in the 2016 volume of Abstract and Applied Analysis.
In the paper, Kantrowitz and Michael M. Neumann of Mississippi State University explore connections between completeness of an ordered field and the validity of the series tests of Dirichlet, Dedekind and Abel.
The authors show that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, that none of the three is valid in any proper subfield of the real numbers. For an arbitrary ordered field, it turns out that in addition to the absolute convergence and comparison tests from calculus, each of the tests of Dirichlet and Dedekind is equivalent to Cauchy completeness for the field.