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

Am Tue, 17 Dec 2024 11:30:46 +0100 schrieb WM:

On 17.12.2024 00:57, Richard Damon wrote:

On 12/16/24 3:59 AM, WM wrote:

On 15.12.2024 22:14, Richard Damon wrote:

On 12/15/24 2:44 PM, WM wrote:

On 15.12.2024 13:54, Richard Damon wrote:

>
You can't "name" your dark numbers,

because they are dark.
|ℕ \ {1, 2, 3, ...}| = 0 cannot be accomplished by visible numbers
because ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

Which just shows that the full set in infinte, and any member in it
is finite, and not the last member.

Many members can be subtracted individually but infinitely many
members cannot be subtracted individually. They are belonging to the
set. They are dark.

Sure an infinite number of members can be subtracted individually,

An unbounded number can be subtracted individually.

As long as it is finite.

However, if all are
subtracted individually, then a last one is subtracted. That cannot
happen.

Whatever do you mean by that? There is no last to inf.many. „All” are
not finite.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.