Allan Wechsler <acwacw@gmail.com> wrote:

I think the generalization to unrestricted arithmetic is an overreach. From any integer A, you can generate any other with an expression of the form (A+A+...+A)/A.

Oops. Good catch. What if I restrict it to arithmetic that mentions each element at most once? Another generalization of my original problem (no element is the sum or difference of two elements, and no element is an integer multiple of another element) is to apply it, not to positive integers, but to a finite or better yet infinite dense set of reals.