On the number of finite additive 2-bases

TL;DR

This paper presents a simple probabilistic proof that the number of finite additive 2-bases grows exponentially, offering an alternative to complex analytic methods.

Contribution

It provides a direct, elementary probabilistic proof of exponential growth, improving understanding of finite additive 2-bases without complex analysis.

Findings

Number of finite additive 2-bases grows exponentially.

Elementary probabilistic proof replaces complex analytic techniques.

Simplifies understanding of the growth behavior.

Abstract

The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short proof using elementary probabilistic arguments.