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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 20 Jan 2025 13:07:03 -0500
Organization: i2pn2 (i2pn.org)
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In-Reply-To: <vmlfqn$34j33$1@dont-email.me>

On 1/20/25 7:33 AM, WM wrote:
> On 19.01.2025 14:29, FromTheRafters wrote:
>> WM formulated the question :
>>> 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.
>>
>> This makes no sense.
> 
> It is impossible.

Because logic that insists on dealing with an INFINITE set one by one is 
illogical except for a being that is itself INFINITE and thus capable of 
INFINITE action.

>>
>>>>> 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.
>>
>> No, they are the same size when it is shown there is at least one 
>> bijection.
> 
> Every element of the bijection has almost all elements as successors. 
> Therefore the bijection is none.

Nope, the logic that can't see the completion at infinity is broken.

> 
>>> All natnumbers in bijections have ℵ₀ not applied successors.
>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>> Only potential infinity is applied.
>>
>> You mean that only finite sets are involved.
> 
> Of course Infinitely many successors prevent that their predecessors are 
> infinitely many.
> 
> Regards, WM
>