Universal entire functions that define order isomorphisms of countable real sets

TL;DR

This paper discusses how universal entire functions can serve as order isomorphisms between any two countable dense subsets of real numbers, extending Cantor's classical result.

Contribution

It demonstrates that universal entire functions can universally realize order isomorphisms between countable dense real sets, providing a functional perspective on Cantor's theorem.

Findings

Universal entire functions can define order isomorphisms between countable dense sets.

Such functions extend Cantor's classical order isomorphisms.

The approach unifies order theory and complex analysis.

Abstract

In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism, which is the restriction of a universal entire function.