Hindman's theorem: Difference between revisions
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New page: '''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspac... |
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'''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain an infinite-dimensional [[combinatorial subspace]], | '''Hindman's theorem''': If <math>[2]^\omega := \bigcup_{n=0}^\infty [2]^n</math> is finitely colored, then one of the color classes contain all elements of an infinite-dimensional [[combinatorial subspace]] which contain the digit 1, and such that none of the fixed digits of this subspace are equal to 1. | ||
The generalization of this theorem | The generalization of this theorem which replaces 2 with larger k is [[Carlson's theorem]]. Hindman's theorem also implies [[Folkman's theorem]]. | ||
Latest revision as of 03:06, 21 May 2009
Hindman's theorem: If [math]\displaystyle{ [2]^\omega := \bigcup_{n=0}^\infty [2]^n }[/math] is finitely colored, then one of the color classes contain all elements of an infinite-dimensional combinatorial subspace which contain the digit 1, and such that none of the fixed digits of this subspace are equal to 1.
The generalization of this theorem which replaces 2 with larger k is Carlson's theorem. Hindman's theorem also implies Folkman's theorem.
