The Riemann Hypotheses: A Lesson in Universal Paradoxes that Lead to the Axiom of Choice – A Path of Unexpected Outcomes

The Riemann Hypothesis, in the article “A view on how to solve it”, challenges the schema of Russell’s Paradoxes through its result. This paper presents, in three segments, how the paradoxes can be viewed. In each segment, paradoxes are introduced to force a deeper look into the area of discourse. This main issue embraces the entire essay as it progresses to different aspects of this work. The first segment outlines the original naïve set concept and schema. The second segment submits the naïve set in the context of functional reasoning, which is a derivation of common sense and reason. Common sense will show that the empty set is irrelevant when functional reasoning, in its core derivation, is considered. Core derivation imposes the Gödel arguments for the existence of God. Thus, these sets of axioms and theorems strengthen the axiom of choice set theory and expose mathematics as the transport mechanism to touch upon the state of consciousness in its understanding of the universe as an evolving entity. Furthermore, the eloquent design of the universe in the quantum sphere of interaction is partly intrinsic to internal awareness of the self. Notwithstanding, the external makeup of human beings is influenced deeply by the classical knowledge of the world. Finally, the third segment, the functional reasoning, introduces Artificial Intellig ence and sets the stage for the Peano Axiom-Theory. The latter sets the stage for limits and quantifiers, which will open the door for omega, the recursive schema associated with a limit point.