Cantor's Dilemma

74 points · 12 comments · view on lemmy.world

12 Comments

ns1@feddit.uk · 28 pts · 178d (9 replies)

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.

brian@lemmy.ca · 14 pts · 178d (2 replies)

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 (4 replies)

Ackshually the text says that A is at least ℵ_2 so it could be way more

ns1@feddit.uk · 3 pts · 178d (3 replies)

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.

eah@programming.dev · 2 pts · 177d (1 reply)

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
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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
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