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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This kind of thread is why I duck out of casual maths discussions as a maths PhD.
The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles. Completely intuitive to someone who’s taken first year undergraduate logic and calculus courses. Completely unintuitive to the lay person, and 100 lay people can come up with 100 different wrong conclusions based on incorrect rationalisations of the statement.
I’ve made an effort to just not participate since back when people were arguing Rick and Morty infinite universe bollocks. “Infinite universes means there are an infinite number of identical universes” really boils my blood.
It’s why I just say “algebra” when asked what I do. Even explaining my research (representation theory) to a tangentially related person, like a mathematical physicist, just ends in tedious non-discussion based on an incorrect framing of my work through their lens of understanding.
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.