Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logicDate : 13. Dec 2024, 13:11:35
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <c6b624cb0b1b55d54aab969ee5b4e283ec7be3cd@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
User-Agent : Mozilla Thunderbird
On 12/12/24 5:06 PM, WM wrote:
On 12.12.2024 18:48, Mikko wrote:
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?
>
No, there is no such set. This is proven by my black hats = numbers of the form 10n: For every interval [1, n] the relative covering is at most 1/10. And more than all intervals are not available to supply numbers of the form 10n.
Regards, WM
No, it proves your logic doesn't have infinite sets.
Note, the pairing is not between some elements of N that are also in D, with other elements in N, but the elements of D and the elements on N.
You just don' understand what it means to PAIR elements of two sets.
Sorry, you are just that dumb.
…