Re: Ultimate debunking of Cantor's Theory

On Jul 13, 4:22 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
You cannot prove the existence of an actually infinte set.

You can't prove the existence of the infinite set N
of natural numbers? Of course you can, as follows:

Assume the contrary, that N is finite. It would then have
a largest element L, by the definition of N, which is that
it is comprised of the elements of the sequence 1, 2, 3, ...
(or if you prefer, 1, (1+1), (1+1+1), ...).

But for every n in N, n+1 is also a natural number.
Thus L+1 is a natural number, which contradicts
the assumption that L is the largest element of N.

Therefore the proposition that N is not infinite is
false.

.