You write: "A set is denumerable (contains a denumerable amount of members) if its members can be mapped by some rule or rules, one to one, with the positive integers, and that set can contain either a finite or infinite amount of members." You still don't get it, or else you're just having your fun with me. Any denumerable set S, like the set of positive integers with which S is equinumerous, is infinite. How many times must I say that?
I proved that the set {0,1,2,3,...} of natural numbers is infinite. I also proved that the set of natural numbers is the same size as the set {1,2,3,...} of positive integers. Do you want me also to prove that the set of positive integers is infinite? (I surely hope not.)