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http://hdl.handle.net/11320/19591Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Pąk, Karol | - |
| dc.date.accessioned | 2026-01-09T10:39:37Z | - |
| dc.date.available | 2026-01-09T10:39:37Z | - |
| dc.date.issued | 2025 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 33, Issue 1, Pages 1-10 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/19591 | - |
| dc.description.abstract | This paper sets out to formalize the concept of the square root as proposed by Clive Bach in the section entitled Properties of Division in Conway’s book. The proposed construction extends the classical approach to the square root of real numbers to include both infinitely large and infinitely small numbers. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | pl |
| dc.subject | surreal number | pl |
| dc.subject | Conway’s game | pl |
| dc.subject | square root | pl |
| dc.title | Surreal Numbers: A Study of Square Roots | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2025 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 4.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2025-0001 | - |
| dc.description.Affiliation | Faculty of Computer Science, University of Białystok, Poland | pl |
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| dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6. | pl |
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| dc.description.references | Harry Gonshor. An Introduction to the Theory of Surreal Numbers. London Mathematical Society Lecture Note Series, 110. Cambridge University Press, 1986. ISBN 0521312051. | pl |
| dc.description.references | Donald E. Knuth. Surreal Numbers: How Two Ex-students Turned on to Pure Mathematics and Found Total Happiness. Addison-Wesley, 1974. | pl |
| dc.description.references | Lionel Elie Mamane. Surreal numbers in Coq. In Jean-Christophe Filliatre, 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 | 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. Conway numbers – formal introduction. Formalized Mathematics, 31(1): 193–203, 2023. doi:10.2478/forma-2023-0018. | pl |
| dc.description.references | Karol Pąk. Inverse element for surreal number. Formalized Mathematics, 32(1):65–75, 2024. doi:10.2478/forma-2024-0005. | pl |
| dc.description.references | Karol Pąk. Integration of game theoretic and tree theoretic approaches to Conway bers. Formalized Mathematics, 31(1):205–213, 2023. doi:10.2478/forma-2023-0019. | pl |
| dc.description.references | Karol Pąk. The ring of Conway numbers in Mizar. Formalized Mathematics, 31(1): 215–228, 2023. doi:10.2478/forma-2023-0020. | pl |
| dc.description.references | Alex Ryba, Philip Ehrlich, Richard Kenyon, Jeffrey Lagarias, James Propp, and Louis Kauffman. Conway’s mathematics after Conway. Notices of the American Mathematical Society, 69:1145–1155, 2022. doi:10.1090/noti2513. | pl |
| dc.description.references | Dierk Schleicher and Michael Stoll. An introduction to Conway’s games and numbers. Moscow Mathematical Journal, 6:359–388, 2006. doi:10.17323/1609-4514-2006-6-2-359-388. | pl |
| dc.description.references | Dominik Tomaszuk, Łukasz Szeremeta, and Artur Korniłowicz. MMLKG: Knowledge graph for mathematical definitions, statements and proofs. Scientific Data, 10(1), 2023. doi:10.1038/s41597-023-02681-3. | pl |
| dc.description.references | The Univalent Foundations Program. Homotopy Type Theory: Univalent Foundations of Mathematics. https://homotopytypetheory.org/book, Institute for Advanced Study, 2013. | pl |
| dc.description.references | Makarius Wenzel, Lawrence C. Paulson, and Tobias Nipkow. The Isabelle framework. In Otmane Ait Mohamed, C´esar Mu˜noz, and Sofi`ene Tahar, editors, Theorem Proving in Higher Order Logics, pages 33–38. Springer Berlin Heidelberg, 2008. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 33 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 1 | pl |
| dc.description.lastpage | 10 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0002-7099-1669 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2025, Volume 33, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Surreal_Numbers_A_Study_of_Square_Roots.pdf | 327,88 kB | Adobe PDF | Otwórz |
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