Oh, I absolutely love the surreal numbers! The surreals are a superset of the reals, but that's not why I think they are interesting. In mainstream pure mathem

Oh, I absolutely love the surreal numbers! The surreals are a superset of the reals, but that's not why I think they are interesting. In mainstream pure mathematics, you first create the naturals (whole numbers). Then from there you create the rationals, as fractions of naturals. Then from there you can create the reals as infinite sequences of rationals. This works, but it is arguably inelegant. We like to say naturals are a subset of rationals, and rationals are a subset of reals. But by this construction they're not ontologically the same. (We can of course find a subset of the reals that look like the rationals, etc., but they aren't identical, only equivalent.) In contrast, the surreal numbers are all constructed in one go. Very elegant.