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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 11 Dec 2024 19:38:40 -0500
Organization: i2pn2 (i2pn.org)
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On 12/11/24 9:04 AM, WM wrote:
> On 11.12.2024 01:25, Richard Damon wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 10.12.2024 13:19, Richard Damon wrote:
>>>
>>>>
>>>> The pairing is between TWO sets, not the members of a set with itself.
>>>
>>> The pairing is between the elements. Otherwise you could pair R and Q by
>>> simply claiming it.
>>> "The infinite sequence thus defined has the peculiar property to contain
>>> the positive rational numbers completely, and each of them only once at
>>> a determined place." [Cantor] Note the numbers, not the set.
>>
>> TWO different sets, not the elements of a set and some of the elements of
>> that same set.
> 
> In mathematics, a set A is Dedekind-infinite (named after the German 
> mathematician Richard Dedekind) if some proper subset B of A is 
> equinumerous to A. [Wikipedia].
> 
> Regards, WM
> 

So? That isn't what Cantor was talking about in his pairings (and in 
fact needs the finding of a Cantor like bijection or the similar to show 
"equinumerous")

Yes, that is one test for infinite, but doesn't let you define the scale 
of infinite.

And that shows that the subset of N of the number that are 0 mod 10 
being able to be mapped 1:1 t the full set of N, shows that N *IS* 
Dedekind-infinite, but NONE of your subset on the way showed it, because 
they were not infinite. Thus showing that the infinite set that is "at 
the limit" of a sequence of finite sets, can have different properties 
than ALL of the finite sets in the sequence.

So, you are just proving your arguement is blown up.