Uloženo v:
| Hlavní autor: | |
|---|---|
| Médium: | Recurso digital |
| Jazyk: | |
| Vydáno: |
Zenodo
2025
|
| Témata: | |
| On-line přístup: | https://doi.org/10.5281/zenodo.17469735 |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
Obsah:
- This paper explores the geometric properties inherent in the algebraic structure of set operations, specifically complementation and intersection. We posit that the repeated application of these operations on subsets of a universal set generates a structure whose qualitative features are analogous to those found in hyperbolic geometry. By modeling the power set as a complemented distributive lattice (a Boolean algebra), we define a notion of distance based on the operational path length between elements. We demonstrate that sequences of intersections and complementations can lead to an exponential divergence of distinct elements, a hallmark of negative curvature. This divergence is analyzed by examining paths on the Hasse diagram of the Boolean lattice, which can be interpreted as a discrete space. The core thesis is that the process of logical refinement through intersection and categorical negation via complementation inherently creates a space of possibilities that expands hyperbolically. This perspective offers a novel geometric interpretation of logical operations and suggests that the abstract space of set-theoretic relations exhibits non-Euclidean characteristics. The implications of this model are discussed in the context of information theory, computational complexity, and the fundamental nature of logical spaces.