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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It was probably mentioned in other comments, but some infinities are "larger" than others. But yes, the product of the two with the same cardinal number will have the same
Yes, uncountably infinite sets are larger than countably infinite sets.
But these are both a countably infinite number of bills. They're the same infinity.
I think quite some people heard of the concept of different kinds of infinity, but don't know much about how these are defined. That's why this meme should be inverted, as thinking the infinities described here are the same size is the intuitive answer when you either know nothing or quite something about the definition whereas knowing just a little bit can easily lead you to the wrong answer.
As the described in the wikipedia article in the top level comment, the thing that matters is whether you can construct a mapping (or more precisely, a bijection) from one set to the other. If so, the sets/infinities are of the same "size".
Yeah, inverting it is a good idea, truly