Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 30. Nov 2024, 11:00:25
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <bdbc0e3d-1db2-4d6a-9f71-368d36d96b40@tha.de>
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User-Agent : Mozilla Thunderbird
On 29.11.2024 22:50, FromTheRafters wrote:
WM wrote on 11/29/2024 :
The size of the intersection remains infinite as long as all endsegments remain infinite (= as long as only infinite endsegments are considered).
Endsegments are defined as infinite,
Endsegments are defined as endsegments. They have been defined by myself many years ago.
all of them and each and every one of them.
The set ℕ = {1, 2, 3, ..., n, n+1, ...} cannot be divided into two consecutive infinite sets. As long as all endsegments are infinite, they contain an infinite subset of ℕ. Therefore all indices are the finite complement of ℕ.
The intersection is empty.
Try to understand inclusion monotony. The sequence of endsegments decreases. As long as it has not decreased below ℵo elements, the intersection has not decreased below ℵo elements.
Regards, WM
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