6 papers
A density version of a theorem of Banach
David A. Ross
The S-measure construction from nonstandard analysis is used to prove an extension of a result on the intersection of sets in a finitely-additive measure space. This is then used t…
Egyptian fractions on groups
David A. Ross
Results about the structure of the set of Egyptian fractions on the line are extended to subsets of topological groups.
Nonstandard arguments for results about infinite systems of equations in infinitely many variables
David A. Ross
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
Linear equations and multiplicative polynomial equations in infinitely many variables
Melvyn B. Nathanson, David A. Ross
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every…
Yet another proof that the roots of a polynomial depend continuously on the coefficients
David A. Ross
The roots of a complex polynomial depend continuously on the coefficients; that is, an infinitesimal perturbation of the coefficients results in an infinitesimal perturbation of th…
Continuity of the roots of a polynomial
Melvyn B. Nathanson, David A. Ross
Let be an algebraically closed field with an absolute value. This note gives an elementary proof of the classical result that the roots of a polynomial with coefficients in …