Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 12. Dec 2024, 23:03:51
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vjfmk7$2upa9$2@dont-email.me>
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User-Agent : Mozilla Thunderbird
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
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