Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : FTR (at) *nospam* nomail.afraid.org (FromTheRafters)
Groupes : sci.mathDate : 02. Dec 2024, 12:53:14
Autres entêtes
Organisation : Peripheral Visions
Message-ID : <vik73d$3a9jm$1@dont-email.me>
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User-Agent : MesNews/1.08.06.00-gb
Chris M. Thomasson brought next idea :
On 11/30/2024 3:12 AM, WM wrote:
On 30.11.2024 11:57, FromTheRafters wrote:
WM explained :
On 29.11.2024 22:50, FromTheRafters wrote:
WM wrote on 11/29/2024 :
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The size of the intersection remains infinite as long as all endsegments remain infinite (= as long as only infinite endsegments are considered).
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Endsegments are defined as infinite,
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Endsegments are defined as endsegments. They have been defined by myself many years ago.
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As what is left after not considering a finite initial segment in your new set and considering only the tail of the sequence.
Not quite but roughly. The precise definitions are:
Finite initial segment F(n) = {1, 2, 3, ..., n}.
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Finite? Huh? The natural numbers don't stop at n! WTF!!!! Lay off the drugs.
That ordered set has a first element namely '1' and a last element, namely 'n' so yes, it is finite.
Endsegment E(n) = {n, n+1, n+2, ...}
This is his definition of endsegment, which as almost anyone can see, has no last element, so yes it is infinite. He says 'infinite endsegment' as if there were a choice, only to add confusion.
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