I know it seems intuitive but assuming that a property holds for n=infinity because it holds for all n<infinity would literally break math and it really doesn’t make much sense when you think about it more than a minute. Here’s an easy counterexample: n is finite.
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humanspiral@lemmy.ca 3 weeks agoI side with you, though the experts call me stupid for it too.
if for all n < infinity, one set is double the size of another then it is still double the size at n = infinity.
stevedice@sh.itjust.works 3 weeks ago
calcopiritus@lemmy.world 3 weeks ago
You’re not stupid for it. Since it makes sense.
However, due to the way we “calculate” the sizes of infinite sets, you are wrong.
Even integers and all integers are the same infinity.
But reals are “bigger” than integers.