numbers Directory Reference

Directory dependency graph for numbers:

Files
	approx.cppm
	Compatibility bridge for IEEE approximation policies.
	boolean.cppm
	Formal definition of the Boolean system 𝔹 within the numeric ontology.
	cardinality.cppm
	Re-export of dedekind.sets:cardinality with numbers-level proofs.
	collatz.cppm
	Bounded Collatz reachability — a §4 relational exhibit on ℕ.
	complex.cppm
	Minimal complex wrapper for experimental reintegration.
	constants.cppm
	Reserved for Dedekind-cut realisations of named reals (empty).
	cut.cppm
	The genuine real: a decidable Dedekind cut on \(\mathbb{Q}\).
	ieee.cppm
	Bridge from numerical carriers into the upstream IEEE core module.
	integer.cppm
	Minimal number taxonomy concepts for reintegration.
	lattice.cppm
	Integer lattices in ℝ_d and ℝ_dⁿ.
	mandelbrot.cppm
	Core Mandelbrot recurrence helpers over complex carriers.
	natural.cppm
	The Dictionary of Species (The Registry).
	numbers.cppm
	Level -1 to 8: The Numerical Tower (ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ).
	quadratic.cppm
	\(\mathbb{Q}(\sqrt D)\) — a genuine, decidable quadratic real field.
	quaternion.cppm
	The Quaternion Division Ring (ℍ).
	rational.cppm
	ℚ — rationals as numerator/denominator pairs.
	real.cppm
	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>.
	real_bridge.cppm
	The Birkhoff S leg \(\mathbb{Q}\hookrightarrow\mathbb{R}\): a genuine monic homomorphism into the \(\mathbb{Q}(\sqrt2)\) coat-hanger, with computed witnesses, plus its graph \(\Gamma=\operatorname{graph}(\text{embed})\subseteq\mathbb{Q}\times \mathbb{R}\) reifying the arrow relationally.
	scalars.cppm
	Semirings as the formal algebraic basis for scalar number systems.
	symbolic.cppm
	Symbolic constants ($\sqrt{2}$, …) as Dedekind cuts.