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

On 12/6/24 4:01 AM, WM wrote:

On 06.12.2024 00:48, Richard Damon wrote:

On 12/5/24 11:08 AM, WM wrote:

On 05.12.2024 13:26, Richard Damon wrote:
>

Which ones can not be "taken" or "given".

>
Those with less than infinitely many successors. Cantor claims that all numbers are in his bijections. No successors remaining.

 

Which since such numbers don't exist,

 If so, then infinity cannot be used completely.
"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)]
None is missing, let alone a natural number or infinitely many successors.
 Regards, WM
 

Why do you say that? Your problem is you think that a complete infinite set is just finite, and thus your logic is just broken.
Complete means it contains all of the values, and if those values are unbounded, then the set doesn't contain a bound for them, and thus not a "last" for them.
This is part of the problem Aristotle was pointing out on trying to work with "Complete" sets that are infinite, that we, as finite beings, can't actually comprehend that unboundedness, as thus have misconceptions of what it "must" be like, which leads us to finding "inconsistencies".
Those inconsistencies aren't in the sets themselves, but in our understanding of them.
Aristotle realized that his logic system could not handle the logic of the complete unbounded set, but you apparently are stuck in that problem, and have let your mind be blown up by it.