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

On 1/25/25 6:14 AM, WM wrote:

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:

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

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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.

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

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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, ...} = { }.

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No, set theory claims that the set is infinite.

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

Nope, maybe means YOUR logic can't acheive actual infinity, and thus blows up when you assume it.

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.

And all Natural Numbers are finite, but form an actually infinite set.
That your logic can't handle actually infiite sets is YOUR problem, and the fact you don't understand that limitation just shows you are too stupid to know your ignorance.
There is no problem using all the Aleph_0 successor, it just means you need to use logic that can handle that.
It isn't the Numbers that change to be use collectively, it is the logic on those numbers that change. Thus no Natural Number needs to be dark, you just need to use logic that can handle infinite sets.

 Regards, WM