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).

I 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, but it is behind a registration wall.

I'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.