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

On 1/17/25 2:34 PM, WM wrote:

Am 17.01.2025 um 15:52 schrieb Richard Damon:

On 1/17/25 8:00 AM, WM wrote:

 

By logic I mean logic. Since the small numbers are always covered by the greater FIS=ONs, the smaller FISONs can be dropped. Either the complete set ℕ is produced by one FISON, which then is not finite and therefore is not a FISON, or it is not produced by FISONs.

>
It is produced by the INFINITE set of FISONs,

All which are smaller than the greatest are useless. That should even be understood by a very limited brain. There is no greatest. Therefore all are useless.
 Regards, WM

So, you agree that your logic makes everything worthless.
Since I hope you agree that being able to do simple math is useful, and thus small numbers are useful even if we can't find the biggest.
THus, your false premise that without a biggest, the smaller are worthless is just incorrect, and thus your conclusion is incorrect.
It may be that without being able to have a biggest Natural Number you think that it makes that set worthless, but that is just your error.
The problem is that a logic that can only work if it can find the "last" number of a set is itself worthless if the sets you are trying to deal with are infinite, so don't have that property.
So, all you are doing is proving that your own logic is faulty and worthless if you want to deal with infinite sets.
There isn't anything wrong with the infinite sets, as with a PROPER logic, they fully work, it is just your broken, and ill-defined, logic that you have your problems.