Conway Numbers – Formal Introduction

Pole DC	Wartość	Język
dc.contributor.author	Pąk, Karol	-
dc.date.accessioned	2024-01-25T11:09:24Z	-
dc.date.available	2024-01-25T11:09:24Z	-
dc.date.issued	2023	-
dc.identifier.citation	Formalized Mathematics, Volume 31, Issue 1, Pages 193-203	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/15856	-
dc.description.abstract	Surreal numbers, a fascinating mathematical concept introduced by John Conway, have attracted considerable interest due to their unique properties. In this article, we formalize the basic concept of surreal numbers close to the original Conway’s convention in the field of combinatorial game theory. We define surreal numbers with the pre-order in the Mizar system which satisfy the following condition: x≤ y iff Lᵪ≪ {y} ∧ {x}≪Rᵧ.	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)	pl
dc.rights.uri	https://creativecommons.org/licenses/by-sa/3.0/	pl
dc.subject	surreal numbers	pl
dc.subject	Conway’s game	pl
dc.subject	Mizar	pl
dc.title	Conway Numbers – Formal Introduction	pl
dc.type	Article	pl
dc.rights.holder	© 2022 The Author(s)	pl
dc.rights.holder	CC BY-SA 3.0 license	pl
dc.identifier.doi	10.2478/forma-2023-0018	-
dc.description.Affiliation	Faculty of Computer Science, University of Białystok, Poland	pl
dc.description.references	John Horton Conway. On Numbers and Games. A K Peters Ltd., Natick, MA, second edition, 2001. ISBN 1-56881-127-6.	pl
dc.description.references	Peter Dybjer. A general formulation of simultaneous inductive-recursive definitions in type theory. The Journal of Symbolic Logic, 65(2):525–549, 2000. doi:10.2307/2586554.	pl
dc.description.references	Philip Ehrlich. Conway names, the simplicity hierarchy and the surreal number tree. Journal of Logic and Analysis, 3(1):1–26, 2011. doi:10.4115/jla.2011.3.1.	pl
dc.description.references	Philip Ehrlich. The absolute arithmetic continuum and the unification of all numbers great and small. The Bulletin of Symbolic Logic, 18(1):1–45, 2012. doi:10.2178/bsl/1327328438.	pl
dc.description.references	Philp Ehrlich. Number systems with simplicity hierarchies: A generalization of Conway’s theory of surreal numbers. Journal of Symbolic Logic, 66(3):1231–1258, 2001. doi:10.2307/2695104.	pl
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Mizar in a nutshell. Journal of Formalized Reasoning, 3(2):153–245, 2010.	pl
dc.description.references	Lionel Elie Mamane. Surreal numbers in Coq. In Jean-Christophe Filliâtre, Christine Paulin-Mohring, and Benjamin Werner, editors, Types for Proofs and Programs, TYPES 2004, volume 3839 of LNCS, pages 170–185. Springer, 2004. doi:10.1007/11617990_11.	pl
dc.description.references	Robin Nittka. Conway’s games and some of their basic properties. Formalized Mathematics, 19(2):73–81, 2011. doi:10.2478/v10037-011-0013-6.	pl
dc.description.references	Steven Obua. Partizan games in Isabelle/HOLZF. In Kamel Barkaoui, Ana Cavalcanti, and Antonio Cerone, editors, Theoretical Aspects of Computing – ICTAC 2006, volume 4281 of LNCS, pages 272–286. Springer, 2006.	pl
dc.description.references	Karol Pąk. Prime representing polynomial. Formalized Mathematics, 29(4):221–228, 2021. doi:10.2478/forma-2021-0020.	pl
dc.description.references	Karol Pąk. Prime representing polynomial with 10 unknowns. Formalized Mathematics, 30(4):255–279, 2022. doi:10.2478/forma-2022-0021.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	31	pl
dc.description.issue	1	pl
dc.description.firstpage	193	pl
dc.description.lastpage	203	pl
dc.identifier.citation2	Formalized Mathematics	pl
dc.identifier.orcid	0000-0002-7099-1669	-
Występuje w kolekcji(ach):	Artykuły naukowe (WInf) Formalized Mathematics, 2023, Volume 31, Issue 1

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