Re: Ultimate debunking of Cantor's Theory

In article <1184400384.279727.37760@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 14 Jul., 00:50, Calvin <cri...@xxxxxxxxxxxxxx> wrote:
On Jul 13, 12:52 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

On 11 Jul., 16:20, Calvin <cri...@xxxxxxxxxxxxxx> wrote:
The original post doesn't restrict set theory to finite
sets. It says that only sets which are finite exist.
Obviously natural numbers exist, and can be used for
example to count the words in this post. Since they
exist, and there are supposedly only a finite number
of them, then there must be a largest one.

That is a naive misunderstanding.

comp.mail.eudora.mac > I hope you understood that my words, "there are
supposedly only a finite number of them," did not
mean that I supposed such a thing. I was stating
the proposition that was to be disproved.

To spell it out clearly: There is only a limited number of natural
numbers. Nevertheless there is no largest one among them.


While there is only a limited number of names (including descriptions)
for natural numbers, or anything else, for that matter, in standard
mathematics, there can exist naturals without names, and rationals
without names, and reals without names, and all sorts of other unnamed
things.

So that WM is barking up the wrong tree to claim that such a limit on
names enforces a limit on numbers. it only limits our ability to name
numbers.
.

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