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A DYNAMICAL PROOF OF VAN DER WAERDEN’S THEOREM, SECOND APPROACH

In this lecture, the second approach of Van Der Waerden’s theorem will be presented. It is based on Birkhoff’s theorem which will also be proved. The essence of Van Der Waerden’s theorem is that if the set of natural numbers N is partitioned in some way into finitely many classes in any way whatever, then one of these classes necessarily contains arbitrarily long arithmetic progressions.