The Mathematics of Quantification, and the Rudiments Of the Ternary Logical States of the Binary Systems
This paper, opening with the historical that documents the source of the Binary Enumeration Error, utilizes the proof of 'Fermat's Last Theorem' (Normative References - [1], [2] and [3]), the Mathematics of Quantification, and the Logic of Set Theory, to prove that the Binary System represents an Alternate Mathematical Field, which is Closed and Finite. That is, using the Elementary Laws of Algebra, with the Basic Principles from Analytic Geometry, provides the final clarification simplifying the proof for the correction of the Counting Errors and the Logical Foundation for the New Binary System. And more importantly, this also establishes the basic foundational principles for 3 State Ternary Logic. In other words, using an askew, or mathematically incorrect Binary System, defined as the misinterpretation of ZERO, sustains the Counting Error (an Accumulating Propagation) levying a substantial loss of IP Addresses in the IPv4 IP Specification, affecting as well, the Address Pool Total for the IPv6 Specification. Hence, from the foregoing foundation an unquestionable proof concludes; the Elementary Mathematical 'Resolution of the Counting Error in the Binary System' - [4. IANA Considerations].