The infinite form of Ramsey's theorem says that if the -element subsets of an infinite set are finitely colored, then some infinite subset has all its -element subsets in one color.
Ramsey's theorem is a fundamental result in combinatorial mathematics and graph theory that addresses the conditions under which order must appear in a large enough structure. The theorem essentially states that in any sufficiently large graph, one can find certain types of complete subgraphs.
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