Another Definition for Ramsey Numbers R (p, q)=r (p-1, q) (2≤p≤q)

We introduce an Idea or a concept of restricted coexistence. By the restricted coexistence, the Ramsey number R(p,q) is defined equivalently as r(p-1,q), that is, R(p,q) = r(p-1,q), where r(p-1,q) is a least integer that has coexistence restricted to the parameters p-1,q with q >= p >= 2. From this, some basic properties about Ramsey numbers are obtained, for instance, R(p,q) > R(p-1,q+1), where p, q are integers with q >= p >= 3, and so on.