Van Der Wardern's theorem gives the number of ways to color one subset of these numbers, and this result is generalized by the Szemeredi theorem.
Van Der Wardern's theorem gives the number of ways to color one subset of these numbers, and this result is generalized by the Szemeredi theorem. The Eisenstein ones are imaginary numbers that lie in the quadratic field "Q extension square root of negative 3", and the Gaussian ones lie in "Q extension square root of negative 1". This set of numbers is a cyclic group under addition with cardinality Aleph-null, and a mapping from the real numbers to them is given by the floor function. Usually denoted by a blackboard "Z", FTP, name this set of numbers which consists of zero, the positive whole numbers, and the negative whole numbers.
Van Der Wardern's theorem gives the number of ways to color one subset of these numbers, and this result is generalized by the Szemeredi theorem.
{Integers} (Accept “{Positive Integers}” before Eisenstein)