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Results tagged with surreal-numbers
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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.
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Accepted
What surreal numbers are representable by Red-Blue Hackenbush games?
All surreal numbers are representable by a Red–Blue Hackenbush game. This is discussed in On Numbers and Games, although it is left to the reader to fill in the details of the proof for the transfini …
- 82.6k
13
votes
Integration in the surreal numbers
In a recent article in the Notices of the AMS, Philip Ehrlich briefly describes some progress in this area. Below is a relevant excerpt from the article.
Conway originally expressed doubt that “reaso …
- 82.6k
11
votes
What's wrong with the surreals?
Conway himself lists a few disadvantages in On Numbers and Games, Chapter 2.
One that can be dealt with quickly is that it is quite tricky to make the process stop after constructing the reals! W …
- 82.6k