real.cppm File Reference

The real line: ℝ (the coat-hanger — a set-indexed field over the order-complete carrier QuadraticReal<2>) and the machine ambient ℝ_d over the finite doubles 𝕃<double>. More...

#include <concepts>
#include <type_traits>
import dedekind.numbers:rational;
import dedekind.sets;
import dedekind.category;
import dedekind.order;
import dedekind.morphologies;
import dedekind.algebra;

Include dependency graph for real.cppm:

Namespaces
namespace	dedekind::numbers

Typedefs
using	dedekind::numbers::machine_real_scalar = double

Variables
constexpr auto	dedekind::numbers::ℝ
	The canonical real-number universe ℝ = 𝔸<QuadraticReal<2>, Boole, ℶ_1> — the coat-hanger.
constexpr auto	dedekind::numbers::ℝ_d
	The machine-real ambient: the finite doubles 𝕃<double>.

Detailed Description

The real line: ℝ (the coat-hanger — a set-indexed field over the order-complete carrier QuadraticReal<2>) and the machine ambient ℝ_d over the finite doubles 𝕃<double>.

@partition :real

Copyright

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

Note

"Die Zahlen sind freie Schöpfungen des menschlichen Geistes." ("Numbers are free creations of the human mind.") – Richard Dedekind, Was sind und was sollen die Zahlen? (1888)