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Results tagged with surreal-numbers
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user 7092
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.
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What do we know about the computable surreal numbers?
I did indeed find the (or at least a) definition of $\sqrt{x}$ for surreal $x$ in On Numbers And Games (page 22 of the second edition). It looks like this:
$$\sqrt{x}=y=\left\{\sqrt{x^L}, \dfrac{x+y^L …
- 1,951