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

On 12/7/24 4:31 PM, Chris M. Thomasson wrote:

On 12/7/2024 4:20 AM, Richard Damon wrote:

On 12/7/24 5:44 AM, WM wrote:

On 06.12.2024 14:30, joes wrote:

Am Thu, 05 Dec 2024 17:04:58 +0100 schrieb WM:

On 05.12.2024 13:56, joes wrote:

Am Thu, 05 Dec 2024 12:42:17 +0100 schrieb WM:

>

But every number you can take belongs to a vanishing subset of ℕ.

What does that have to do with the ability to be "chosen"?

It is impossible to choose a number outside of a tiny subset.

Duh. There are no other numbers.

>
May be. My statements however concern completed infinity. The subset is never complete.
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Regards, WM
>

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And thus the limit of the subsets is not complete either, per your logic of a limit of constants is always that same constant. Thus, your trying to define the complete infinity just fails.

 WM seems to think that "completed" means there simply must be a largest natural number? I can only guess here.

He seems to think that Completed means all of them, but then he assumes that if you have "all" of a set, that set must have a last element.
This comes from the fact that the only sets he can have are finite, and complete finite sets have a last element.
He just doesn't get that a complete infinite set doesn't necessarily have a "last" element in it, because that concept is just unimaginable to his tiny brain.