Re: Ultimate debunking of Cantor's Theory

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.

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.

There is a limited number of bits.
From these bits you can form natural numbers.
The magnitude of these numbers is merely
limited by the ingeniousity to introduce suitable
abbreviations.

So, let's say that everyone in the universe finally
runs out of suitable abbreviations, and the last
natural number so abbreviated is recorded according
to those abbreviations. Let's now agree to refer
to that number as George. What is George + 1?

.

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