Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/13/24 12:10 PM, WM wrote:

On 13.12.2024 13:11, Richard Damon wrote:

On 12/13/24 4:57 AM, WM wrote:

"erhalten wir nicht bloß eine einzige unendliche ganze Zahl, sondern eine unendliche Folge von solchen, die voneinander wohl unterschieden sind und in gesetzmäßigen zahlentheoretischen Beziehungen zueinander sowohl wie zu den endlichen ganzen Zahlen stehen."

>
Which, if I understand the context he says this in, are the transfinite numbers.
>
The "infinite integers" are not claimes to be part of the Natural Numbers, but of the extended set nof numbers created by the rules of transfinite mathematics.

 In German he does not say integer but whole number. Of course they are not natural numbers, but numbers without decimal point.
 Regards, WM

And thus, them being transfinite numbers is not unreasonable.
That you confuse them with finite values is understandable considering your general confusion about such issues.
Note, you introduced this based on sequences of FINITE numbers, which these are not.