An Interesting Perspective to the P versus NP Problem

We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k ≤ n) polynomial functions on n always yields a polynomial function, we prove that P = NP , considering the maximum clique problem. And with the proposition that the sum of k polynomial functions may yield an exponential function, we prove that P 6= NP by constructing an abstract decision problem. Furthermore, we conclude that P = NP and P 6= NP if and only if the above propositions hold, respectively.