Monotone subsequence via ultrapower

Błaszczyk Piotr; Kanovei Vladimir; Katz Mikhail G.; Nowik Tahl

doi:10.1515/math-2018-0015

Open Mathematics (Mar 2018)

Monotone subsequence via ultrapower

Błaszczyk Piotr,
Kanovei Vladimir,
Katz Mikhail G.,
Nowik Tahl

Affiliations

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

DOI: https://doi.org/10.1515/math-2018-0015
Journal volume & issue: Vol. 16, no. 1
pp. 149 – 153

Abstract

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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.

Published in Open Mathematics

ISSN: 2391-5455 (Online)
Publisher: De Gruyter
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://www.degruyter.com/journal/key/math/html

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