I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
this post was submitted on 06 Jan 2024
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Correct me if I'm wrong, but isn't it that a simple statement(this is more worth than the other) can't be done, since it isn't stated how big the infinities are(as example if the 1$ infinity is 100 times bigger they are worth the same).
Sorry if you've seen this already, as your comment has just come through. The two sets are the same size, this is clear. This is because they're both countably infinite. There isn't such a thing as different sizes of countably infinite sets. Logic that works for finite sets ("For any finite a and b, there are twice as many integers between a and b as there are even integers between a and b, thus the set of integers is twice the set of even integers") simply does not work for infinite sets ("The set of all integers has the same size as the set of all even integers").
So no, it isn't due to lack of knowledge, as we know logically that the two sets have the exact same size.
OK thanks for your explanation.