Erdös -Szekeres定理

Erdős–Szekeres theorem

theorem that sufficiently long sequences of numbers have long monotonic subsequences

In mathematics, the Erdős–Szekeres theorem asserts that, given and , any sequence of distinct real numbers with length at least contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem.