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

On 1/14/25 3:34 AM, WM wrote:

On 14.01.2025 09:02, Moebius wrote:

Am 13.01.2025 um 21:55 schrieb Chris M. Thomasson:

On 1/13/2025 9:17 AM, WM wrote:

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doubling of all natural numbers creates numbers larger than ω.

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Idiotic nonsense.

 Possibly. But it is a direct consequence of actual = completed infinity. If all natural numbers fill the space between 0 and ω such that nothing more fits in between, then nothing more fits in between.

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And nothing more needs to fit inbetween, as double evey Natural Number is an already existing Natural Number, so none were created.
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All of those results are natural numbers. They were already there...

 Nonsense.

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Yes, YOU are Nonsense.
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Indeed. (At least in the context of classical mathematics/set theory.)

 Doubling changes the number. If all were there already, then all are changed. ∀n ∈ ℕ: 2n > n.

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Nope, that is your stupidity talking, doubling infinity keeps it at infinity.
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Using symols:
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          An e IN: n*2 e IN .

 True for all definable natnumbers. Wrong for natnumbers > ω/2.

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There are no Natural Numbers > omega / 2 as Omega / 2 is just omega.
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You are just showing that you don't know what infinity actually is.