A variant of the proof of Van der Waerden's theorem by Furstenberg

Özkurt, Ali Aslan2022-12-262022-12-262021https://doi.org/10.31801/cfsuasmas.901214http://hdl.handle.net/20.500.12575/86428Let 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].enVan der Waerden Theorem, dynamical system, metric spaceA variant of the proof of Van der Waerden's theorem by FurstenbergArticle106510721303-5991