Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.math
Date : 14. Dec 2024, 23:20:51
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vjl0c3$6aeq$1@dont-email.me>
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
User-Agent : Mozilla Thunderbird
On 12/14/2024 3:10 AM, joes wrote:
Am Thu, 12 Dec 2024 23:03:51 +0100 schrieb WM:
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.
YOU try to map N onto itself.
 
Is this cheating?
{ 1 + 0, 2 + 0, 3 + 0, ... }
lol.

Date Sujet#  Auteur
14 Dec 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2joes
14 Dec 24 `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1Chris M. Thomasson

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