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van der Waerden's theorem

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.

Proper noun

van der Waerden's theorem

  1. 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.

Origin of van der Waerden's theorem

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

Questions about van der Waerden's theorem

What does van der Waerden's theorem mean?
Van der Waerden's theorem means 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.
What part of speech is van der Waerden's theorem?
Van der Waerden's theorem is a proper noun.

Words near van der Waerden's theorem in the dictionary

  1. van der Waals gases
  2. Van der Waals law
  3. van der Waals radius
  4. van der Waals strain
  5. van der Waals volume
  6. van der Waerden's theorem
  7. van der Woude syndrome
  8. Van Devender
  9. Van Devenders
  10. Van Diemen Gulf
  11. Van Diemen's Land

Source and license

Adapted from Wiktionary: van der Waerden's theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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