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TopicsErdős–Szekeres monotone subsequence theorem Combinatorics

Every sequence of k^2+1 distinct reals has a monotone subsequence of length k+1, and k^2+1 is optimal.

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given a sequence of {k^2+1} distinct real numbers, one can find a subsequence of length {k+1} which is either increasing or decreasing; and that one cannot improve the {k^2+1} to {k^2}

https://terrytao.wordpress.com/2025/12/08/the-story-of-erdos-problem-126/extraction 0.95

Tao recalling the Erdős–Szekeres theorem in the introduction of the problem's history.

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Created by extractor · Sep 13, 2026. Every judgment on this page is accompanied by a reasoning trace.