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

On 12/18/24 2:06 PM, WM wrote:

On 18.12.2024 13:29, Richard Damon wrote:

On 12/17/24 4:57 PM, WM wrote:

 

>
You claimed that he uses more than I do, namely all natural numbers.

>
Right, you never use ALL the natural numbers, only a finite subset of them.

 Please give the quote from which you obtain a difference between
"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." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]
and my "the infinite sequence f(n) = [1, n] contains all natural numbers n completely, and each of them only once at a determined place."
 Regards, WM
 

How is your f(n) an "infinite sequence, since n is a finite number in each instance.
NONE of your f(n) contains *ALL* natural numbers, since no "n" is the highest natural number, since suc a number doesn't exist,
Your problem is you just don't understand what "infinity" is, and seem to think it is just some unimaginably bit but finite number, which is just wrong.