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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The โ set between 0 and 1 never reaches 1 or 2 therefore the set of real numbers is valued more. You're limiting the value of the set because you're never exceeding a certain number in the count. But all real numbers will (eventually in the infinite) get past 1. Therefore it is higher value.
The example they're trying to say is there are more real numbers between 0 and 1 than there are integers counting 1,2,3... In that case the set between 0 and 1 is larger but since it never reaches 1 it has less value.
Infinity is a concept so you can't treat it like a direct value.