7 citations · 13 across the 4 of their papers we have counts for
4 papers
Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus
James F. Hall, Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of several equivalent statements} borrowed from algebra, real analy…
Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus
James F. Hall, Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis,…
Completeness of Ordered Fields
James Forsythe Hall
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature…
Another Proof of the Existence a Dedekind Complete Totally Ordered Field
James F. Hall, Todor D. Todorov
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently…