Archimedean / ordered-field convergence stubs. More...

#include <cmath>
#include <concepts>
#include <type_traits>
import dedekind.sets;
import dedekind.sequences;
import dedekind.category;

Include dependency graph for archimedean.cppm:

Classes
struct	dedekind::morphologies::CauchyPath< T >
struct	dedekind::morphologies::singleton_image_breadcrumb::Successor< N >
	The successor \(S : N \to N\) as an arrow, over any carrier with the NNO step: the one spelling of the Peano successor where an `IsArrow` is needed (`image`, `graph`, the NNO witness), in place of a struct per site. More...

Namespaces
namespace	dedekind::morphologies::singleton_image_breadcrumb

Concepts
concept	dedekind::morphologies::IsCyclic
	\emph{Operational} duck-typed check that `T` carries the member API of a cyclic structure: `T::Domain` alias, `T::generator()` returning a Domain element, and `T::successor(a)` walking the chain.
concept	dedekind::morphologies::IsSimplyInfinite
concept	dedekind::morphologies::IsCyclicRing
concept	dedekind::morphologies::IsOrderedField
concept	dedekind::morphologies::IsArchimedeanField
concept	dedekind::morphologies::IsDedekindCompleteField
concept	dedekind::morphologies::IsMinkowskiSummable

Variables
constexpr auto	dedekind::morphologies::singleton_image_breadcrumb::s0 = η(0)
constexpr auto	dedekind::morphologies::singleton_image_breadcrumb::s1 = image(Successor<int>{}, s0)

Detailed Description

Archimedean / ordered-field convergence stubs.

@partition :archimedean

Copyright: 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

Note: चतुराधिकं शतमष्टगुणं द्वा षष्ठीस्तथा सहस्रद्वयम्। — Aryabhata, Aryabhatiya, Ganitapada 10 (499 CE). [Sanskrit original; Trans: "Add four to 100, multiply by eight, and then add 62,000. This is the measure of the circumference of a circle whose diameter is 20,000." Yields π ≈ 3.1416, accurate to 4 decimal places.]

Classes