elementary set theory - finite and infinite subsets of positive integers

Prove that the set consisting of all subsets(both finite and infinite) of set , P, of positive integers is uncountable using the following approach. First clearly P is countable so we can list all the integers in P and clearly map each element in this list into a subscript of its location in this list. Write down the first 10 elements in this list. Now suppose we can list all subsets of the set, P in another list. Write down an example first 10 elements of this list. Now neatly complete the argument to prove uncountability using both list.