symbolic.cppm File Reference

Symbolic constants ($\sqrt{2}$, …) as Dedekind cuts. More...

#include <cmath>
#include <concepts>
import dedekind.sets;
import dedekind.category;
import dedekind.numbers:complex;

Include dependency graph for symbolic.cppm:

Namespaces
namespace	dedekind::numbers

Functions
template<typename Q>
constexpr auto	dedekind::numbers::Sqrt2_Symbolic ()
template<typename R> requires std::regular<R>
constexpr auto	dedekind::numbers::TranscendentalSet ()
	The Transcendental Set (𝕋).

Variables
template<typename T>
constexpr bool	dedekind::numbers::is_transcendental_v = false
	Trait to mark a species as Transcendental (π, e).

Detailed Description

Symbolic constants ($\sqrt{2}$, …) as Dedekind cuts.

@partition :symbolic

Copyright

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

symbolic__Description

Reifies algebraic real constants as predicate-set lower-cuts (ETCS subobjects of ℚ). The cut is the constant; bounded-precision queries are the only thing that crosses the realisation boundary.

Note

"Wiskunde is een vrije schepping van de menselijke geest, onafhankelijk van de ervaring." [Trans: "Mathematics is a free creation of the human mind, independent of experience."] — L. E. J. Brouwer, paraphrased from Over de grondslagen der wiskunde (Amsterdam, 1907). Brouwer's intuitionist / constructive programme is the methodological ancestor of this partition: the cut is the constant (a free mental construction); bounded-precision queries are the only realisation that crosses the boundary.