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Results tagged with surreal-numbers
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user 75
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.
8
votes
Transcendence degree of the surreals over the subfield generated by the ordinals
The transcendence degree of the surreals over the ordinals is proper class sized. There are many ways of seeing this; here's one. Recall that there is an order-preserving map $x\mapsto \omega^x$ fro …
- 31.2k
9
votes
Accepted
Pontryagin dual of the surreal numbers?
For any infinite cardinal $\kappa$, let $S_\kappa$ be the surreal numbers of rank $<\kappa$, considered as a group under addition and topologized with the order topology (if you want to consider all t …
- 31.2k