“Szemerédi’s theorem”的概念、定义、翻译、参考文献-科学参考

单词	Szemerédi’s theorem
释义	Szemerédi’s theorem Mathematics The theorem shows that a suitably dense subset of the natural numbers contains arbitrarily long arithmetic progressions. The set A ⊆ ℕ needs to satisfy $\begin{matrix} lim sup \\ n \to \infty \end{matrix} \frac{\| A \cap {1, 2, \dots, n} \|}{n} > 0.$ The theorem implies Van der Waerden’s theorem but does not imply the Green-Tao theorem, as the primes do not have positive density. See also Erdős conjecture.
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