Monotone subsequence via ultrapower
arXiv:1803.00312 · doi:10.1515/math-2018-0015
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
7 pages, to appear in Open Mathematics