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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sat, 25 Jan 2025 12:14:18 +0100
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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.

Regards, WM