A low-energy decomposition theorem

TL;DR

This paper proves a decomposition theorem for finite sets of real numbers, splitting them into parts that are either highly non-additive or highly non-multiplicative, revealing structural properties of such sets.

Contribution

It introduces a novel decomposition theorem that separates finite real sets into additive and multiplicative components, advancing understanding of their structural properties.

Findings

Sets can be decomposed into additive and multiplicative parts

The decomposition reveals inherent structural dichotomies

Provides a new tool for analyzing real number sets

Abstract

We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.