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

On 12/15/24 1:57 PM, WM wrote:

On 15.12.2024 13:52, Richard Damon wrote:

On 12/15/24 7:00 AM, WM wrote:

On 14.12.2024 23:04, Jim Burns wrote:

 

If ψ is finite, then ψ+1 is finite.
If ψ+1 is finite, then ψ+2 is finite.

>
Yes, that is the potentially infinite collection of definable numbers. But it explains nothing.

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That is the collection of numbers known as the Natural Numbers, so I guess you are admitting that your "Definable Numbers" include *ALL* of the Natural Numbers

 Dark numbers are required to empty ℕ by |ℕ \ {1, 2, 3, ...}| = 0. All definable numbers fail: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
 Regards, WM
 

And why do you need to do that?
All you are doing is showing that you don't understand that an infinite set doesn't have a "last" member, and is catagorically bigger than any finite set.
Thus, all you have done is shown that your logic is just totally exploded leaving a "dark hole" behind from its nuclear explosion into smithereens from the contradictions you make it generate.
Sorry, but that is the truth, which seems to be beyond your ability to understand.