Re: Ultimate debunking of Cantor's Theory

On 16 Jul., 07:20, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1184550638.931818.34...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

Calvin <cri...@xxxxxxxxxxxxxx> wrote:
After finally accepting everything else, I was still
having trouble with the notion that one couldn't use
'not having a largest element' to prove that a set is
infinite, if it is a subset of the naturals, integers,
rationals, or reals, all of which are one-dimensional
number systems.

IF one has a non-empty ordered set without a largest element, one can
easily prove

But IF one has an empty non-ordered set with a largest element, what
can one prove then? That question resembles on IF one has an infinite
set with a last element, like {1,2,3,..., omega} of order type omega +
1, is this set infinite?

Regards, WM

.

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