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This would make a lot more sense to me if "nothing" and "nothing" were instead "-inf" and "+inf" Some other comments clarify that "nothing" is more accurately
by howunfortunate 14d ago
This would make a lot more sense to me if "nothing" and "nothing" were instead "-inf" and "+inf"
Some other comments clarify that "nothing" is more accurately "the empty set". This is helpful because at first I wrongly synonomized "nothing" with zero. But now I get tripped up on the "between" language. Maybe it's a lack of background in sets, but I don't know what "between" implies for an integer (zero) and a set (the empty set).
- danabramov 14d agoI didn't want to introduce the notion of infinity because there are actual "infinite numbers" on the surreal number line. I've kind of tried to have both the simplicity of set-theoretic definition and the intuition of the number line, and slightly bungled the exposition. I hope the newly added diagram helps. My favorite intro to surreal numbers is https://www.infinitelymore.xyz/p/surreal-numbers https://www.infinitelymore.xyz/p/surreal-numbers, but it is behind a registration wall.
- mcintyre1994 14d agoI'm not a mathematician and "nothing" doesn't really make sense for me either. But I guess the problem with inf might be that it'd be strange to get +2 as the next thing between +1 and +inf, while getting +1.5 between +1 and +2.
- danabramov 14d agoIt's more that surreal numbers already include infinities like ω, ω + 1, and so on, so "inf" felt like a concept I want to avoid. The actual description is set-theoretic and uses empty sets there ("nothing to the left", "nothing to the right") so I took that a bit too literally.