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

On 1/10/25 11:42 AM, WM wrote:

On 10.01.2025 14:09, joes wrote:

Am Fri, 10 Jan 2025 10:52:46 +0100 schrieb WM:

 

Hint: The set of all natural numbers, IN, does not change.

So all natural numbers are fixed. Then for every point on the ordinal
line it is determined whether there is a natural number. Although we
cannot determine it because most are dark.

There are no points without numbers.

 As I said. You can prove it when doubling all elements of the set {1, 2, 3, ..., ω}. The regular distance of next neighbours remains as a conserved property in correct mathematics.
 Regards, WM

>

 

One problem with your claim, is that the last element of your set, doesn't HAVE a defined distance between it and a "neighbour", since there isn't a neighbor to it in the sequence, so your premise that you are claiming is just a falsehood.
So, you are just proving your stupidity.