Re: Incompleteness of Cantor's enumeration of the rational numbers

On 20.11.2024 19:12, joes wrote:

Am Wed, 20 Nov 2024 17:51:19 +0100 schrieb WM:

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"

 You are once again lacking in precision:

It was Cantor who said the above. There is no lack of precision.

every natural is finite and thus
countable.

According to Cantor there is no number missing, let alone infinitely many. Set theory claims that all natural numbers can be counted to such that no successors remain. That is false.
Regards, WM