<abstract xmlns="http://www.w3.org/1999/xhtml">

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: <italic>x</italic> ⩽ <italic>y</italic> iff <italic>Lx</italic> ≪ {<italic>y</italic>} <italic>Λ</italic> {<italic>x</italic>} ≪ <italic>Ry</italic>.
</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 Lx ≪ {y} Λ {x} ≪ Ry.

Conway Numbers – Formal Introduction

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 Public License.

{"article-title":"Conway Numbers \u2013 Formal Introduction"}

Surreal numbers, a fascinating mathematical concept introduced by John Conway, have attracted considerable interest due to their unique properties. In this...

康威数字–正式介绍

在线发布:2023年12月31日

页面范围： 193 - 203

认可的:2023年12月12日

内政部： https://doi.org/10.2478/forma-2023-0018

关键词
超实数,康威的游戏,米扎尔

©2023 Karol Pąk，由Sciendo出版

本作品根据Creative Commons Attribution-ShareAlike 3.0公共许可证授权。