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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Thu, 12 Dec 2024 19:48:05 +0200
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On 2024-12-11 14:04:30 +0000, WM said:

> 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].

Do you happen to know any set that is Dedekind-infinite?

-- 
Mikko