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An Introduction to Conway's Games and Numbers

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arxiv math/0410026 v2 pith:RR6EUCT6 submitted 2004-10-01 math.CO

Dierk Schleicher , Michael Stoll This is my paper · ORCID
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keywords gamesnumberstheorycombinatorialconwaygameintroductionbeautiful
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This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD of numbers, (4) ordinal numbers, (5) games and numbers, (6) infinitesimal games, (7) impartial games.

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  1. On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory

    math.LO 2025-01 conditional novelty 3.0 of 10

    Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.

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