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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
📌 3 Key Takeaways
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Objective & Hypothesis:Let RR be a commutative ring with identity.
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Key Findings & Data:In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of RR, we will define a metric on RR using them.
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Conclusion & Impact:Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Van der Waerden Theorem · dynamical system · metric space
Abstract
Let RR be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of RR, we will define a metric on RR using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
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Cite This Article
EYİDOĞAN, S., ÖZKURT, A. A. (2021). A variant of the proof of Van der Waerden's theorem by Furstenberg. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 2, 1065–1072. https://ajindex.com/articles/746720