Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 29. Nov 2024, 11:57:13
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vic6m9$11mrq$4@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 29.11.2024 09:54, FromTheRafters wrote:
WM expressed precisely :
But as long as infinitely many natnumbers have not left the endsegments, they stay inside all of them. And many are the same for all endsegments. Therefore the intersection of infinite endsegments is infinite.
Natural numbers don't "leave", sets don't change.
Call it as you like. Fact is that the function of endsegments is losing elements. The limit is the empty endsegment.
You don't 'run out of indices' or elements to index.
As long as infinitely many natnumbers are within endsegments, there are only finitely many indexed endsegments. All endsegments containing infinitely many natnumbers are finitely many.
Regards, WM
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