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

<p>In this article, we develop our formalised concept of Conway numbers as outlined in [<xref ref-type="bibr" rid="j_forma-2023-0019_ref_009">9</xref>]. We focus mainly pre-order properties, birthday arithmetic contained in the Chapter 1, <italic>Properties of Order and Equality</italic> of John Conway’s seminal book. We also propose a method for the selection of class representatives respecting the relation defined by the pre-ordering in order to facilitate combining the results obtained for the original and tree-theoretic definitions of Conway numbers.</p>
</abstract>

In this article, we develop our formalised concept of Conway numbers as outlined in [9]. We focus mainly pre-order properties, birthday arithmetic contained in the Chapter 1, Properties of Order and Equality of John Conway’s seminal book. We also propose a method for the selection of class representatives respecting the relation defined by the pre-ordering in order to facilitate combining the results obtained for the original and tree-theoretic definitions of Conway numbers.

Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers

Formalized Mathematics

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

{"article-title":"Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers"}

In this article, we develop our formalised concept of Conway numbers as outlined in [9]. We focus mainly pre-order properties, birthday arithmetic contained in...

Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers

Published Online: Dec 31, 2023

Page range: 205 - 213

Accepted: Dec 12, 2023

DOI: https://doi.org/10.2478/forma-2023-0019

Keywords
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.

Integration of Game Theoretic and Tree Theoretic Approaches to Conway Numbers

Published Online: Dec 31, 2023

Page range: 205 - 213

Accepted: Dec 12, 2023

DOI: https://doi.org/10.2478/forma-2023-0019

Keywordssurreal 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.

Keywords
surreal numbers, Conway’s game, Mizar