Monotone subsequence via ultrapower

Monotone subsequence via ultrapower

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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Bibliographische Detailangaben
Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2018-03, Vol.16 (1), p.149-153
Hauptverfasser: Błaszczyk, Piotr, Kanovei, Vladimir, Katz, Mikhail G., Nowik, Tahl
Format: Artikel
Sprache:eng
Schlagworte:
26A06
26A48
26E35
40-99
Compactness
Monotone subsequence
Ordered structures
Saturation
Ultrapower
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Beschreibung
Zusammenfassung: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.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2018-0015