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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 12 Dec 2024 23:03:51 +0100
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On 12.12.2024 18:29, Jeff Barnett wrote:
> On 12/12/2024 6:59 AM, joes wrote:
>> Am Tue, 10 Dec 2024 18:01:04 +0100 schrieb WM:
>>> 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.
>> What Richard meant: do not confuse the set being mapped with the one 
>> being
>> mapped onto.
> 
> But that's sort of what mappings are for! Aren't they?

Dedekind maps the elements of a subset to the elements of its superset. 
Same do I.

Regards, WM