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Results for “distinction” 4 papers
Numeral systems. Radix choice, positional notation, numeral design Tagged papers: 30.
Number Systems as Stratified Distinction Operations: An Enclosure Hierarchy over the Mark
The conventional tower of number systems—$\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}\subset\mathbb{C}$—augmented by the $p$-adic fields $\mathbb{Q}_{p}$ and the adele ring $\mathbb{A}$ is usually presented as a sequence of completions without a unifying generative principle.…
The Number Builder: Enclosure Sequences in the Laws of Form Calculus as a Constructive Route to Computable Reals
We address the gap that no minimal, mark‑based formalism has been shown to generate all computable reals. We formalize enclosure sequences as finite Laws of Form (LoF) expressions equipped with a computable re‑entry schedule, define an interpretation that maps each unfolding to a rational…
The Calculus of Re-Entrant Distinctions: A Unified Treatise on the Loop, the Tree, and the Constants of Self-Reference
This treatise develops a single thesis: that the primitive act of distinction — the drawing of a boundary between marked and unmarked — generates, under the discipline of re-entry and linear resource management, the constants $e$ and $\pi$, the landscape of completions of the rational numbers, the…
NUMERATA: A Multi-Axis Framework for Evaluating Numeral Systems
How should numeral systems be evaluated? NUMERATA v1.0 proposed an 8-axis framework spanning structural, cognitive, and design dimensions. v2.0 extends this foundation in two directions. First, we integrate a Distinction Calculus for Numbers (DCN) — a formal arithmetic grounded in…
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