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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, 9 Dec 2024 19:45:28 -0500
Organization: i2pn2 (i2pn.org)
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On 12/9/24 8:04 AM, WM wrote:
> On 09.12.2024 13:03, Richard Damon wrote:
>> On 12/9/24 4:04 AM, WM wrote:
>>> On 08.12.2024 19:01, Jim Burns wrote:
>>>
>>>> You (WM) are considering
>>>> infinite dark.finite.cardinals,
>>>> which do not exist.
>>>>
>>> Then analysis is contradicted in set theory.
>>> ∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
>>> The limit of the left-hand side is empty, the limit of the right-hand 
>>> side is full, i.e. not empty.
>>> I do not tolerate that.
>>>
>> By your logic, 1 equals 0, 
> 
> No, that are two different sequences.
> 
> Regards, WM
> 

But since both 0^x and x^0 as x approaches 0 approach 0^0, your logic 
says that 0^0 is both 0 and 1.

Just because you have a sequence, doesn't mean you can talk about the 
end infinite state at the "end" of the sequence.

That is EXACTLY the logic you are trying to use, you have two sequences 
that seem to go to the same infinte set at the end, and these both seem 
to result in different values when they are only treated as finite 
sequences.

Thus, your "logic" also shows that 1 == 0, and thus your logic has blown 
itself up.