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

On 1/16/25 8:28 AM, WM wrote:

On 15.01.2025 23:31, Jim Burns wrote:

On 1/15/2025 1:17 PM, WM wrote:

On 15.01.2025 16:16, Jim Burns wrote:

On 1/14/2025 4:07 AM, WM wrote:

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Half are new.

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A step is never from finite to infinite.

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∀n ∈ ℕ: 2n =/= n.

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A step is never from finite to infinite.

 Then there is no complete set ℕ. Then new numbers can be inserted, which are the result of doubling but have not been doubled.
 Regards, WM
 

No, it means your logic can't handle the complete set of N. No new numbers can be inserted, as if you HAD the complete infinity, they would all be there, the full *INFINITE* (and thus without end) set of them.
There wouldn't be new number to insert, as they would all have been there already.
The fact that you think more can be created, just means you never understood how to have all of them in the first place.
It may be true that with YOUR deficient logic, you can't have the complete set of Natural Numbers, but that isn't a flaw in the set of Natural Numbers, it is in your logic, which is just based on Naive assumptions that just blow it up when misused.