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

Am Mon, 25 Nov 2024 13:18:28 +0100 schrieb WM:

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.>

Not all, but every.

But there is no finite set with ALL natural numbers.
Like usual, you mess up with your qualifiers.

ℕ is fixed, that means |ℕ| is fixed.

What does that have to do with it?

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.

It has the same cardinality.

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.

Why not just directly take N, made up of finite numbers?

WIth infinity, Any and All are different qualifiers.

Use them to increase your qualification.

*quantifiers

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.