van der Waerden's theorem

proper noun

In Ramsey theory, a theorem stating that, for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.

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Meanings

proper noun
  1. mathematicsIn Ramsey theory, a theorem stating that, for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.

Origin

Named after the Dutch mathematician B. L. van der Waerden.

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Cite this entry
APA

van der Waerden's theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/van%20der%20Waerden's%20theorem

MLA

“van der Waerden's theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/van%20der%20Waerden's%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “van der Waerden's theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/van%20der%20Waerden's%20theorem.

Source: van der Waerden's theorem on Wiktionary, CC BY-SA 4.0.