Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : mikko.levanto (at) *nospam* iki.fi (Mikko)
Groupes : sci.logicDate : 12. Dec 2024, 18:48:05
Autres entêtes
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Message-ID : <vjf7kl$2s7e5$1@dont-email.me>
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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
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