If n=Ri(r;k1,k2,...kr), r-colering:(）h ie{1,2,...,r}and Sc[n withS= such that entire is colored by i Theorem(Ramsey 1930) Ri(r;k1,k2,...,kr)is finite.If n ≥ Rt(r; k1, k2, ... , kr), Theorem (Ramsey 1930) Rt(r; k1, k2, ... , kr) is finite. ∀ r-coloring ∃i∈{1,2,...,r} and S⊆[n] with |S|=ki such that entire f : ￾[n] t ￾ ￾ [r] ￾S t ￾ is colored by i