Re: Incompleteness of Cantor's enumeration of the rational numbers

On 24.11.2024 20:14, Richard Damon wrote:

On 11/24/24 12:32 PM, WM wrote:

The finite sets contain all hats because all natural numbers and all 10n are in finite sets. No hat is outside.>

 But there is no finite set with ALL natural numbers.

ℕ is fixed, that means |ℕ| is fixed.

 Like usual, you mess up with your qualifiers.

Limit theory only works if the limit actually exists

>
If limits exist at all, then the limit of the sequence 1/10, 1/10, 1/10, ... does exist.

 But the concept of 1/10th of an infinte set does not exist..

It does.

 

You can get things that APPEAR to reach a limit, but actually don't.

>
But if infinite sets do exist, then the set ℕ does exist, and all its elements are members of finite intervals (0, n].

 No, any given element is a member of a finite set, but you can't then say that ALL are in such a set.

All are in the union of all finite sets.

 WIth infinity, Any and All are different qualifiers.

Use them to increase your qualification.
Regards, WM