Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 10.01.2025 23:42, joes wrote:

Am Fri, 10 Jan 2025 22:44:31 +0100 schrieb WM:

Yes they can, because there are an infinity of them.

That is wrong. Infinitely many of them can only exist when no natural
natural number is missing an an index.

The naturals *are* the indices of the sequence. And it is infinite.

Not if any natural is missing because it remains in the content.

 

Therefore none can remain in the
content. Therefore your argument is fools crap.

The limit is indeed empty.

There is no limit! All indices are required for bijections. Bijections concern all elements, not limits. In particular a sequence of infinite sets has no empty "limit".
Another theorem of set theory:
An sequence of infinite endsegments can have an empty limit.
Together with this famous one:
A union of FISONs which stay below a certain threshold can surpass that threshold.
Regards, WM