Monotone subsequence via ultrapower

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

doi:10.1515/math-2018-0015

Monotone subsequence via ultrapower

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

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	149-153
Number of pages	5
Journal	Open Mathematics
Volume	16
Issue number	1
DOIs	https://doi.org/10.1515/math-2018-0015
State	Published - 2018

Keywords

Compactness
Monotone subsequence
Ordered structures
Saturation
Ultrapower

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1515/math-2018-0015

Cite this

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title = "Monotone subsequence via ultrapower",

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 = "Compactness, Monotone subsequence, Ordered structures, Saturation, Ultrapower",

author = "Piotr B{\l}aszczyk and Vladimir Kanovei and Katz, {Mikhail G.} and Tahl Nowik",

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year = "2018",

doi = "10.1515/math-2018-0015",

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T1 - Monotone subsequence via ultrapower

AU - Błaszczyk, Piotr

AU - Kanovei, Vladimir

AU - Katz, Mikhail G.

AU - Nowik, Tahl

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Compactness

KW - Monotone subsequence

KW - Ordered structures

KW - Saturation

KW - Ultrapower

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U2 - 10.1515/math-2018-0015

DO - 10.1515/math-2018-0015

M3 - مقالة

SN - 1895-1074

VL - 16

SP - 149

EP - 153

JO - Open Mathematics

JF - Open Mathematics

IS - 1

ER -

Monotone subsequence via ultrapower

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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