I'm writing a paper on the Continuum Hypothesis by Georg Cantor where I support the proposition with pairing, arithmetic, and computability. The logical connectives applied to the natural numbers creates arithmetic and the integers. Since the integers are measure-wise equivalent to the rational numbers there is no set whose cardinality is between Z and R. Furthermore, the arithmetic of the integers and rational numbers leads to real numbers R with the endless number of special ratios known as complex numbers. In short, without binary/boolean architecture there isn't any computability; as such, therefore the cardinality of the continuum is preceded by the integers. The real numbers are then the composition of calculus and the rest of analysis.