Ramsey Theory and Topological Dynamics

Abstract

Van Der Waerden’s theorem says that “If the positive integers are partitioned into two classes then at least one of those classes must contain arbitrarily long arithmetic progression.” A more generalized version of this theorem can be said in the way that “If the set of positive integers are partitioned into r classes then at least one of the class must contain an arithmetic progression of arbitrary finite length.” We will study the proof of this theorem with Ramsey Theory and Topological Dynamics.