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Related to the Hyperreal numbers mentioned in the article is the class of Surreal numbers which have many fun properties. There's a nice book describing them authored by Don Knuth.


The hyperreals and surreals are actually isomorphic under a mild strengthening of the axiom of choice (NBG).

https://mathoverflow.net/questions/91646/surreal-numbers-vs-...

See Ehrlich’s answer.




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