Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : noreply (at) *nospam* example.org (joes)
Groupes : sci.mathDate : 14. Dec 2024, 12:10:43
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <96b2e89299e7f6d24fdde41b3242ece49b6245e2@i2pn2.org>
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User-Agent : Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2)
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.
-- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:It is not guaranteed that n+1 exists for every n.
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)