I'll give this a go. The number of people at A is ℵ2 and at B is 2^ℵ0^. If the continuum hypothesis is true then there are ℵ1 people at B so A has more people, if it is false then either there are more at B or there could be equally many at A and B (if the star axiom is true).
Either way infinitely many people are dying so it's a sad story.
I thought that as well for a while so I was waiting for someone to say that! My claim that A is exactly ℵ2 is based on it saying "unique", meaning there's only 1 cardinality with the property described, between ℵ0 and A (which must be ℵ1). But I agree the wording is not very clear. The version without uniqueness is still a dilemma, it just means that it's also possible for A to be larger than B even if CH is false.
How would you write it? My goal was to write it in a way that would be most understandable to the most people (so, avoid using symbols like ℵ) while still being concise.
Not sure honestly, I can think of alternatives but I don't know if they're better. "Isomorphism of sets" is a fancy way of saying "bijection", and "unique set up to isomorphism" is the same as "unique cardinal" but as you say it's better to use terms that everyone knows. It might just be that "unique" being right at the beginning makes it easy to forget. Decoding the description is a fun part of the problem!
12 Comments
ns1@feddit.uk · 28 pts · 178d
I'll give this a go. The number of people at A is ℵ
2and at B is 2^ℵ0^. If the continuum hypothesis is true then there are ℵ1people at B so A has more people, if it is false then either there are more at B or there could be equally many at A and B (if the star axiom is true).Either way infinitely many people are dying so it's a sad story.
brian@lemmy.ca · 14 pts · 178d
yeah but only one of those options gives you a wicked K/D ratio
eah@programming.dev · 13 pts · 178d
Cantor's Die Lemma
threelonmusketeers@sh.itjust.works · 3 pts · 177d
Multitrack drifting
FishFace@piefed.social · 3 pts · 178d
Ackshually the text says that A is at least ℵ_2 so it could be way more
ns1@feddit.uk · 3 pts · 178d
I thought that as well for a while so I was waiting for someone to say that! My claim that A is exactly ℵ
2is based on it saying "unique", meaning there's only 1 cardinality with the property described, between ℵ0and A (which must be ℵ1). But I agree the wording is not very clear. The version without uniqueness is still a dilemma, it just means that it's also possible for A to be larger than B even if CH is false.eah@programming.dev · 2 pts · 177d
How would you write it? My goal was to write it in a way that would be most understandable to the most people (so, avoid using symbols like ℵ) while still being concise.
ns1@feddit.uk · 3 pts · 177d
Not sure honestly, I can think of alternatives but I don't know if they're better. "Isomorphism of sets" is a fancy way of saying "bijection", and "unique set up to isomorphism" is the same as "unique cardinal" but as you say it's better to use terms that everyone knows. It might just be that "unique" being right at the beginning makes it easy to forget. Decoding the description is a fun part of the problem!
FishFace@piefed.social · 2 pts · 177d
Yeah I noticed that and thought I had deleted my comment! Oh well!
Novocirab@feddit.org · 1 pts · 178d
princess@lemmy.blahaj.zone · 5 pts · 178d
I flip a coin and let the initial conditions of the universe decide.
FishFace@piefed.social · 2 pts · 178d
"up to isomorphism" is weird. I tried they're trying to say a unique cardinal number and by isomorphism they just mean any bijection.
aberrate_junior_beatnik@midwest.social · 2 pts · 176d
If the trolley is traveling at a finite speed, it will end up killing the same number of people either way.
If it's not, I won't have time to flip the switch anyway.
Novocirab@feddit.org · 1 pts · 178d