Proximity Inversion Functions on the Non-Negative Integers

Abstract

We consider functions mapping non-negative integers to non-negative real numbers such that a and a+n are mapped to values at least 1/n apart. In this paper we use a novel method to construct such a function. We conjecture that the supremum of the generated function is optimal and pose some unsolved problems.

20 pages, Latex; v2: Introduction expanded, Proof of main theorem rewritten for clarity, formatting changed