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

WM pretended :

On 25.11.2024 22:05, joes wrote:

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

>

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?

>
It is impossible to add or to delete an element.

However, one can make a new set by considering another element not previously considered in a set, or by not considering one of the previously considered elements. Sets don't change, but new sets can be made.

It is impossible to change |ℕ| by 1 or more.

Right, sets don't change. The set {2,3,4,...} does not equal the set of natural numbers, but |{2,3,4,...}| does equal |N|.
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