SP-TNT 1.0 (English shop)

Eine praxisnahe Modifikation und Erweiterung der Theoria Numerorum Typographica

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To resolve fundamental inconsistencies and logical ambiguities in classical mathematics and physics, a completely gap-free and contradiction-free foundation is required. While the famous typographical number system (“Theoria Numerorum Typographica”, TNT) from Douglas R. Hofstadter’s classic Gödel, Escher, Bach is primarily of philosophical value, this work bridges the gap to a practical, rigorously formal application.

The starting point of the investigation consists of profound physical and mathematical problems surrounding differential operators in mappings with poles and singularities in vector analysis, such as those occurring in the context of point charges involving gradient, divergence, and Laplace operators. Since nature does not feature artificial mathematical jumps, the work establishes a radically watertight formalism that systematically remedies classical flaws—including missing quantifier logic, ambiguous scopes of differential operators, and inconsistencies in coordinate systems.

To achieve this, the expanded SP-TNT system is introduced, featuring a robust quantifier logic with separated symbol sets and strictly defined scopes. Building upon this, the work provides a closed axiomatic system of propositional logic ranging from truth values to formal proof techniques such as the fantasy concept with hierarchical line numbering.

Because precise foundational work also requires the structured integration of quantities, the publication further includes an axiomatic grounding of all major number domains from natural to complex numbers, including set groups, alongside a consistent calculus of units.

Overall, the presented system provides the essential foundation for exact scientific proofs, thereby establishing the methodical basis for forthcoming volumes on theoretical electrodynamics.