Re: Ultimate debunking of Cantor's Theory

One thing that
still bothers me is the claim that showing that a
set does not have a largest element is not a proof of
infinite size.

I understand that plenty of sets without largest
elements are bounded above, but in every case I can
think of (such as the positive rationals strictly
less than 1), the set is infinite. Are there known
counterexamples within the realm of the naturals,
the integers, the rationals, and the reals?

In the case of complex numbers, one can easily
describe finite sets of distinct elements, all having
the same absolute value, and the same would be true
in all such sets of dimension greater than 1.
But for one-dimensional sets, I can't grasp it.

.

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