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

On 24.01.2025 13:29, Richard Damon wrote:

On 1/19/25 5:47 AM, WM wrote:

On 18.01.2025 14:46, Richard Damon wrote:

On 1/17/25 4:56 PM, WM wrote:

>

That "definition" violates to definition that set don't change.

>
So it is. But if infinity is potential, then we cannot change this
in order to keep set theory, but then set theory is wrong.

>
So, you are just agreeing that your logic is based on contradictory
premsises and thus is itself contradictory and worthless.

>
No, set theory claims actual infinity but in fact useses potential
infinity with its "bijections". They contain only natnumbers which
have ℵ₀ successors. If all natural numbers were applied, there would
not be successors:
ℕ \ {1, 2, 3, ...} = { }.

 
No, set theory claims that the set is infinite.

 
But it is only potentially infinite. ℵo successors prevent actual
infinity.

you are trying to use a non-set compatible distinction between actual
and potential infinity

I prove it. Only finite numbers can be chosen individually.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
To have infinitely many would require to use also the ℵo successors.