Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 05. Dec 2024, 20:30:22
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <3af23566-0dfc-4001-b19b-96e5d4110fee@tha.de>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
User-Agent : Mozilla Thunderbird
On 05.12.2024 18:12, Jim Burns wrote:
On 12/5/2024 4:00 AM, WM wrote:
On 04.12.2024 21:36, Jim Burns wrote:
On 12/4/2024 12:29 PM, WM wrote:
[...]
>
No intersection of
more.than.finitely.many end.segments
of the finite.cardinals
holds a finite.cardinal, or
is non.empty.
>
Small wonder.
More than finitely many endsegments
require
infinitely many indices, i.e., all indices.
No natnumbers are remaining in the contents.
⎛ That's the intersection.
And it is the empty endsegment. The contents cannot disappear "in the limit". It has to be lost one by one if ∀k ∈ ℕ : E(k+1) = E(k) \ {k} is really true for all natnumbers.
⎜
Small wonder.
More than finitely many endsegments
require
infinitely many indices, i.e., all indices.
No natnumbers are remaining in the contents.
Yes.
That means an empty endsegment and many having finite contents.
Regards, WM
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