Metamathematical Fundamental Research

The boundary concepts of mathematics—zero and infinity—are not merely numerical abstractions, but fundamental qualities around which formal reasoning itself is organized. While modern mathematics has developed powerful tools to handle these concepts independently, their deeper structural relationship has long remained implicit.

This fundamental research project approached the relationship between zero and infinity not through specific computational techniques, but through meta-level structural considerations. The focus was placed on the dual boundary structure in which these two notions appear as complementary manifestations within a unified conceptual framework.

Within this perspective, zero and infinity were not treated as opposing endpoints, but as two limiting expressions of a single coherent structural order. This shift allowed mathematical meaning to be associated not with isolated values, but with structural transitions and boundary behavior.

A key outcome of the project was the recognition that the relationship between zero and infinity can be interpreted as a stable dual symmetry, rather than a technical anomaly or exceptional case. This symmetry provides a conceptual basis for addressing situations where distinct scales or regimes must be understood within a single descriptive framework.

The research did not aim to introduce new computational methods or formal procedures. Instead, it established a metamathematical orientation in which boundary concepts play an active role in the organization of meaning and structure.

With the completion of the project, the zero–infinity relationship was integrated into the system as a foundational structural symmetry. Detailed formal constructions and algorithmic realizations are intentionally excluded from the public documentation.