The P vs. NP Continuum Hypothesis

Abstract:
This paper presents an isomorphism between the set of problems in P and the Natural Numbers, and an isomorphism between the set of problem in NP and the powerset of the Naturals. Using these isomorphisms the properties of the equivalent classes P and NP are investigated. A property is found which holds for one class but not the other, thus P != NP. The isomorphisms are then used to prove that the Continuum Hypothesis is false because the set of problems overlapping P and NP is empty.