A variant of the proof of Van der Waerden's theorem by Furstenberg
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Date
2021
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Ankara Universitesi
Abstract
Let R be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of R, we will define a metric on R 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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Keywords
Van der Waerden Theorem, dynamical system, metric space