A sum-division estimate of reals

TL;DR

This paper establishes a new inequality relating the sum set and quotient set of a finite set of positive real numbers, providing insights into their combinatorial structure.

Contribution

It introduces a sum-division estimate that bounds the product of sum set squared and quotient set size in terms of the set's cardinality.

Findings

|A+A|^2|A/A|   rac{|A|^4}{4}

Provides a new lower bound linking sum and division operations on reals

Enhances understanding of additive and multiplicative structure of real sets

Abstract

Let $A$ be a finite set of positive real numbers. We present a sum-division estimate: |A+A|^2|A/A|\geq\frac{|A|^4}{4}.