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.
Guy, Winning Ways , 2nd edition, Wellesley, Massachusetts: A
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On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory
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.