Just as van der Waerden's theorem has a stronger "density version" in Szemerédi's theorem, the Hales–Jewett theorem also has a density version. In this strengthened version of the Hales–Jewett theorem, instead of coloring the entire hypercube "W""n""H" into "c" colors, one is given an arbitrary subset "A" of the hypercube "W""n""H" with some given density 0 < δ < 1. The theorem states that if "H" is sufficiently large depending on "n" and δ, then the set "A" must necessarily contain an entire combinatorial line.