The Convergence Morphism (Resolution of the Path). More...
#include <concepts>#include <functional>import dedekind.sequences:path;import dedekind.order;import dedekind.topology;import dedekind.category;
Concepts | |
| concept | dedekind::sequences::HasLimit |
| Species that can resolve a Path into a single point. | |
Functions | |
| template<typename T> requires std::floating_point<T> && IsArchimedean<T> | |
| constexpr T | dedekind::sequences::limit (const Path< T > &s) |
| The Archimedean Limit (lim n->∞ s_n). | |
| constexpr Truth< Boole > | dedekind::sequences::limit (const Path< Truth< Boole > > &s) |
| The Discrete Limit Morphism for Boolean Truth. | |
Detailed Description
The Convergence Morphism (Resolution of the Path).
@partition :limits
limits__Convergence
This partition defines the "Resolution" of a Path into a single point. In the Dedekind structuralist framework, a limit is the terminal state of a sequence as it enters the infinitesimal neighborhood of a species.
We utilize the Archimedean property from (:order) to ensure that the species supports the notion of "stepping" toward an asymptotic horizon.
Wikipedia: Limit of a sequence, Archimedean property, Convergence
- Copyright
- 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.
- Note
- "A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts." – David Hilbert, Mathematical Problems (1900)
Function Documentation
◆ limit() [1/2]
requires std::floating_point<T> && IsArchimedean<T>
|
constexprexport |
The Archimedean Limit (lim n->∞ s_n).
For machine primitives (floating_point), this resolves to the epsilon-stabilized tail of the sequence.
- Template Parameters
-
T A floating-point species satisfying the Archimedean property.
- Parameters
-
s The path (sequence) to be resolved.
- Returns
- The value at the species' asymptotic horizon.
limits__Structuralist_Resolution
In a machine context, we sample the path at the 'asymptotic' horizon of the species.
