Re: Ultimate debunking of Cantor's Theory

On Jul 14, 12:11 am, Proginoskes <CCHeck...@xxxxxxxxx> wrote:
On Jul 13, 3:51 pm, Calvin <cri...@xxxxxxxxxxxxxx> wrote:

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.

Nope. This is the mistake: You are assuming that N can
be constructed in the first place.

I dealt with that in my proof, below, part of which is

"...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), ...)"

That clearly is a valid construction, though it
does not use set theory notation, which no doubt
would make the definition more elegant.

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.


.

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