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Abstracts Mathematics
Completeness Axioms in an Ordered Field
by Louis Marie Carter
| Institution: | North Texas State University |
|---|---|
| Department: | |
| Degree: | |
| Year: | 1971 |
| Keywords: | completeness axioms; ordered field |
| Posted: | |
| Record ID: | 1561157 |
| Full text PDF: | http://digital.library.unt.edu/ark:/67531/metadc131462/ |
Abstract
The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.
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