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Large set (Ramsey theory)
In Ramsey theory, a set ''S'' of natural numbers is considered to be a large set if and only if Van der Waerden's theorem can be generalized to assert the existence of arithmetic progressions with common difference in ''S''. That is, ''S'' is large if and only if every finite partition of the natural numbers has a cell containing arbitrarily long arithmetic progressions having common differences in ''S''.
==Examples==
*The natural numbers are large. This is precisely the assertion of Van der Waerden's theorem.
*The even numbers are large.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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