Partition of a Set Which Contains an Infinite Arithmetic (Respectively Geometric) Progression

2009/11/23 by Florentin Smarandache, Florentín Smarandache, Smarandache, Florentin
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Mathematics and Applications #math.GM #msc:05A18

paper · pdf · doi:10.48550/arxiv.0911.4415

arxiv created 2009/11/23 · arxiv updated 2009/12/08

Abstract

We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two disjoint subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is an arithmetic (respectively geometric) progression.

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