<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...

Conway Numbers – Formal Introduction

Online veröffentlicht: 31. Dez. 2023

Seitenbereich: 193 - 203

Akzeptiert: 12. Dez. 2023

DOI: https://doi.org/10.2478/forma-2023-0018

Schlüsselwörter
surreal numbers, Conway’s game, Mizar

© 2023 Karol Pąk, published by Sciendo

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

Conway Numbers – Formal Introduction

Online veröffentlicht: 31. Dez. 2023

Seitenbereich: 193 - 203

Akzeptiert: 12. Dez. 2023

DOI: https://doi.org/10.2478/forma-2023-0018

Schlüsselwörtersurreal numbers, Conway’s game, Mizar

© 2023 Karol Pąk, published by Sciendo

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

Schlüsselwörter
surreal numbers, Conway’s game, Mizar