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For questions about the surreal numbers, which are a real-closed ordered proper-class-sized field that contains both the real numbers and the ordinal numbers. Thus they contain both infinite numbers (including the ordinals, but also infinite numbers like ω-1 and sqrt(ω)) and infinitesimal numbers (like 1/ω). They can also be identified with a subclass of two-player partisan games.
2
votes
What surreal numbers are representable by Red-Blue Hackenbush games?
If you only allow connected graphs, and in particular do not allow ordinal numbers, the answer is no, unless you assign surreal numbers to Hackenbush games by a means other than induction.
First it's …
20
votes
Accepted
Are Conway's omnific integers the Grothendieck group of the ordinals under commutative addit...
There is an obvious extension of Cantor normal form to the Grothendieck group of the ordinals. Then the standard argument that $\sqrt{x}$ does not lie in the ring $\mathbb Z[x]$ applies to $\sqrt{\ome …