You've got the subset relationships backwards: Reals are a subset of the field of Surreal Numbers which is a subset of the group of Games. (Probably better phra

You've got the subset relationships backwards: Reals are a subset of the field of Surreal Numbers which is a subset of the group of Games. (Probably better phrased as embeddings, rather than subsets, but the point remains...) Note that Games do _not_ form a field: there is no general multiplication operation between arbitrary games.