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A ''corner'' is a subset of <math>[n]^2</math> of the form <math>\{(x,y),(x+d,y),(x,y+d)\}</math> with <math>d\ne 0.</math> One often insists also that d should be positive.

The [[corners theorem]] asserts that for every <math>\delta>0</math> there exists n such that every subset A of <math>[n]^2</math> of density at least <math>\delta</math> contains a corner.

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