Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 20. Nov 2024, 17:51:19
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhl426$5tug$1@dont-email.me>
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On 20.11.2024 15:15, FromTheRafters wrote:
WM explained on 11/20/2024 :
set theory claims that all natural numbers can be counted to such that no successors remain.
No it doesn't.
Even all rationals and algebraics.
"we get the epitome (ω) of all real algebraic numbers [...] and with respect to this order we can talk about the nth algebraic number where not a single one of this epitome has been forgotten"
"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"
Regards, WM