# Corners

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A corner is a subset of $[n]^2$ of the form $\{(x,y),(x+d,y),(x,y+d)\}$ with $d\ne 0.$ One often insists also that d should be positive.
The corners theorem asserts that for every $\delta\gt0$ there exists n such that every subset A of $[n]^2$ of density at least $\delta$ contains a corner.