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

On 19.01.2025 11:42, FromTheRafters wrote:

WM presented the following explanation :

On 18.01.2025 12:03, joes wrote:

Am Fri, 17 Jan 2025 22:56:13 +0100 schrieb WM:

>

Correct. If infinity is potential. set theory is wrong.

And that is why set theory doesn't talk about "potential infinity".

>
Nevertheless it uses potential infinity.

 No, it doesn't.

Use all natnumbers individually such that none remains. Fail.

 

All "bijections" yield the same cardinality because only the potentially infinite parts of the sets are  applied.

 No, it is because these bijections show that some infinite sets' sizes can be shown to be equal even if no completed count exists.

They appear equal because no completed count exists.
All natnumbers in bijections have ℵ₀ not applied successors.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
Only potential infinity is applied.
In actual infinity all natnumbers would be applied:
ℕ \ {1, 2, 3, ...} = { }
But that is not possible in bijections.
Regards, WM