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.
I 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.
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.
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.