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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: Wed, 11 Dec 2024 15:32:32 +0100
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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