Academic Journal
00: The Recursive Zero and the Layered Abstraction of Number
| Τίτλος: | 00: The Recursive Zero and the Layered Abstraction of Number |
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| Συγγραφείς: | Bolter, Barry Brian |
| Συνεισφορές: | Bolter, Barry Brian |
| Στοιχεία εκδότη: | Zenodo |
| Έτος έκδοσης: | 2025 |
| Συλλογή: | Zenodo |
| Θεματικοί όροι: | Recursive zero, Double zero (00), Mathematical abstraction, Logic boundary, Structural recursion, Formal systems, Zero asymmetry, Automata theory, Computational logic, Recursive computation, Meta-neutral element, Type theory, Recursive mathematics, Non-standard number systems, Closure and abstraction, Symbolic logic, Foundations of Mathematics, Logic and Set Theory, Number Theory (Non-standard number systems), Formal Languages and Automata Theory, Theory of Computation, Programming Languages (Semantics, Type Systems), Philosophy of Mathematics, Ontology of Abstraction, Symbolic Reasoning, Recursive Representation Models |
| Περιγραφή: | Title:00: The Recursive Zero and the Layered Abstraction of Number Description:This paper introduces a structurally distinct mathematical entity: recursive zero, denoted as 00. Unlike classical zero (0), which marks termination and nullity, 00 functions as a recursive neutral — a boundary that enables logical recombination and transformation rather than collapse. We demonstrate the operational distinction between 0 and 00 through two formal models: a recursive logic engine and an automata-based system. The paper also explores the implications of this distinction across computation, formal logic, automata theory, algebra, quantum systems, and programming language design. The extended number line is revealed to possess a structural asymmetry across the 00|0 boundary, where the domain left of 00 remains abstract and open, and the domain right of 0 is operationally closed. This asymmetry offers a new lens through which to understand definability, closure, and recursion in foundational mathematics. This is a foundational contribution intended for researchers in mathematics, theoretical computer science, formal logic, and symbolic systems. It may also be of interest to philosophers of mathematics and AI theorists exploring machine-structured reasoning. |
| Τύπος εγγράφου: | text |
| Γλώσσα: | unknown |
| Relation: | https://zenodo.org/records/15667175; oai:zenodo.org:15667175; https://doi.org/10.5281/zenodo.15667175 |
| DOI: | 10.5281/zenodo.15667175 |
| Διαθεσιμότητα: | https://doi.org/10.5281/zenodo.15667175 https://zenodo.org/records/15667175 |
| Rights: | Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.FDC38688 |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.5281/zenodo.15667175 |
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