Monotone subsequence via ultrapower

Piotr Błaszczyk 1 , Vladimir Kanovei 2 , Mikhail G. Katz 3  and Tahl Nowik 3
  • 1 Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland
  • 2 IPPI, Moscow, and MIIT, Moscow, Russia
  • 3 Department of Mathematics, Bar Ilan University, 52900, Ramat Gan, Israel

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.

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