> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.
Got lost here. I think I'm officially too dumb for math.
I made a picture, hope this helps: <a href="https://excalidraw.com/#json=zfKWWn1h7GzdFca6RDdXl,plr_WeaCtvFxbjULFjq6zw" rel="nofollow">https://excalidraw.com/#json=zfKWWn1h7GzdFca6RDdXl,plr_WeaCt...
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 <a href="https://www.infinitelymore.xyz/p/surreal-numbers" rel="nofollow">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.
It'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.
howunfortunate · · focus · HN ↗
Got lost here. I think I'm officially too dumb for math.
danabramov · · focus · HN ↗
Sorry it was confusing.
Edit: the picture is now edited into the article.
howunfortunate · · focus · HN ↗
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 · · focus · HN ↗
My favorite intro to surreal numbers is <a href="https://www.infinitelymore.xyz/p/surreal-numbers" rel="nofollow">https://www.infinitelymore.xyz/p/surreal-numbers, but it is behind a registration wall.
mcintyre1994 · · focus · HN ↗
danabramov · · focus · HN ↗