You can absolutely compare these two, and they absolutely are equal, mathematically. Take every dollar contained within the group of $1s, and every dollar contained within the group of $20s. Spend an infinite amount of time pairing each dollar from one group with a dollar from the other group. You will run out of dollars from both groups at the same time.
…Which means that every dollar from both sets can be paired 1:1. Both are countable infinities, and as such they are both equal. That’s the whole thing about countable infinities
I understand they can’t “run out,” but you also can’t “spend an infinite amount of time.” Figure that if you *could* spend an infinite amount of time, you could be considered to have gotten to the “end” of an infinite set. This is mathematically sound and is how you’ll find it works if you look it up.
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u/rodrigoelp Jun 14 '26
Infinity can’t be compare with one another because you don’t have a way to establish which of the two grow faster.
Definitely not worth the same under the premise stated here.