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Cantor's Dilemma (programming.dev)
submitted 8 months ago by to c/mathmemes@lemmy.blahaj.zone
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[–] 3 points 8 months ago (4 children)

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

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  • [–] 3 points 8 months ago (3 children)

    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.

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  • [–] [S] 2 points 8 months ago (1 child)

    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.

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  • [–] 3 points 8 months ago

    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!

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