Linear equations and multiplicative polynomial equations in infinitely many variables

TL;DR

This paper investigates infinite polynomial equations in infinitely many variables, showing that solutions for all finite subsets imply solutions for the entire infinite set, with implications for understanding infinite systems.

Contribution

It introduces a property linking finite subset solutions to the entire infinite set for polynomial equations in infinitely many variables, advancing the theory of infinite polynomial systems.

Findings

Finite subset solutions imply solutions for the entire infinite set

Establishes conditions under which infinite polynomial systems are solvable

Provides a framework for approximate solutions in infinite systems

Abstract

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a solution for the infinite set of equations.