Monotone subsequence via ultrapower
Classical Analysis and ODEs
2018-05-11 v1 Logic
Abstract
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications. Keywords: ordered structures; monotone subsequence; ultrapower; saturation; compactness
Cite
@article{arxiv.1803.00312,
title = {Monotone subsequence via ultrapower},
author = {Piotr Blaszczyk and Vladimir Kanovei and Mikhail G. Katz and Tahl Nowik},
journal= {arXiv preprint arXiv:1803.00312},
year = {2018}
}
Comments
7 pages, to appear in Open Mathematics