Level -1 to 8: The Numerical Tower (ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). More...

import dedekind.numbers:real_bridge;
import dedekind.order;
import dedekind.topology;

Include dependency graph for numbers.cppm:

Detailed Description

Level -1 to 8: The Numerical Tower (ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ).

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

numbers__Structural_Numerics

"Liczba nie jest tylko wielkością, lecz punktem w sieci powiązań. Zrozumieć liczbę to zrozumieć strukturę, w której ona występuje." (A number is not merely a magnitude, but a point in a network of relations. To understand a number is to understand the structure in which it occurs.) — Zdzisław Pawlak

This module reifies the standard numerical species as formal Categorical objects. Following the Dedekind tradition, we do not treat numbers as "built-in" primitives, but as specific positions within an algebraic and order-theoretic hierarchy.

Note: "Meine Methoden sind wirklich Methoden des Arbeitens und Denkens; deshalb sind sie überall anonym eingedrungen." — Emmy Noether, letter to Helmut Hasse (1931), cited in Auguste Dick, Emmy Noether, 1882-1935 (1981). [Trans: "My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously."]