English

Finitely many implies infinitely many

Combinatorics 2024-09-24 v2

Abstract

Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set II, then it is true for all of II. This paper describes some old and new results on infinite sets of linear and polynomial equations with the property that solutions for all finite subsets of the set of equations implies the existence of a solution for the infinite set of equations.

Keywords

Cite

@article{arxiv.2401.12887,
  title  = {Finitely many implies infinitely many},
  author = {Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:2401.12887},
  year   = {2024}
}

Comments

Minor corrections, 12 pages

R2 v1 2026-06-28T14:24:55.123Z