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Results tagged with surreal-numbers
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user 6794
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.
27
votes
Who discovered the surreals?
If one thinks of the surreal numbers as just a proper-class sized saturated real-closed field, then I think Alling deserves much of the credit for the discovery or invention. He didn't deal with the p …
- 73.1k
13
votes
A question about J.H. Conway's SURREAL NUMBERS
As you said, each surreal number can be regarded as a set, but the collection of all of them is a proper class. The set-theoretic issues involved in "developing the theory of these numbers" are the s …
- 73.1k
9
votes
Accepted
Surreal numbers and large cardinals
I'm not aware of references that use universes in the study of surreal numbers. The reason --- for the non-existence of such references or for my non-awareness of them if they do exist --- is that th …
- 73.1k
7
votes
First-order definable bijection between $P(On)$ (or $No$) and $V$? (Is this equivalent to $V...
$\mathcal P(\text{On})$ has a definable linear ordering, namely the lexicographical one: One set $x$ of ordinals precedes another set $y$ of ordinals iff the first element of their symmetric differenc …
- 73.1k