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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: Wed, 11 Dec 2024 19:32:21 -0500
Organization: i2pn2 (i2pn.org)
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On 12/11/24 9:32 AM, WM wrote:
> On 11.12.2024 03:04, Richard Damon wrote:
>> On 12/10/24 12:30 PM, WM wrote:
>>> On 10.12.2024 13:17, Richard Damon wrote:
>>>> On 12/10/24 3:50 AM, WM wrote:
>>>
>>>>> Two sequences that are identical term by term cannot have different 
>>>>> limits. 0^x and x^0 are different term by term.
>>>>
>>>> Which isn't the part I am talking of, it is that just because each 
>>>> step of a sequence has a value, doesn't mean the thing that is at 
>>>> that limit, has the same value.
>>>
>>> Of course not. But if each step of two sequences has the same value, 
>>> then the limits are the same too. This is the case for
>>>   (E(1)∩E(2)∩...∩E(n)) and (E(n)).
> 
>> But the limit of the sequence isn't necessary what is at the "end" of 
>> the sequence.
> 
> The end of the sequence is defined by ∀k ∈ ℕ : E(k+1) = E(k) \ {k}.
> 
> Regards, WM
> 

None of which are an infinite sets, so trying to take a "limit" of 
combining them is just improper.