Conway Numbers – Formal Introduction

IF 1 Q1 MATHEMATICS Formalized Mathematics Pub Date : 2023-09-01 DOI:10.2478/forma-2023-0018
Karol Pąk
{"title":"Conway Numbers – Formal Introduction","authors":"Karol Pąk","doi":"10.2478/forma-2023-0018","DOIUrl":null,"url":null,"abstract":"Summary 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 Lx ≪ {y} Λ {x} ≪ Ry.","PeriodicalId":42667,"journal":{"name":"Formalized Mathematics","volume":"254 1","pages":"193 - 203"},"PeriodicalIF":1.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Formalized Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/forma-2023-0018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Summary 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 Lx ≪ {y} Λ {x} ≪ Ry.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
康威数字 - 正式介绍
摘要 超实数是约翰-康威提出的一个引人入胜的数学概念,因其独特的性质而备受关注。在本文中,我们将超实数的基本概念形式化,使其接近于组合博弈论领域中最初的康威约定。我们定义了米扎(Mizar)系统中带有前序的超实数,它满足以下条件:x ⩽ y iff Lx ≪ {y}Λ {x} ≪ Ry。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Formalized Mathematics
Formalized Mathematics MATHEMATICS-
自引率
0.00%
发文量
0
审稿时长
10 weeks
期刊介绍: Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.
期刊最新文献
On the Formalization of Gram-Schmidt Process for Orthonormalizing a Set of Vectors On Bag of 1. Part I Introduction to Graph Enumerations Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method Elementary Number Theory Problems. Part VII
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1