Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : FTR (at) *nospam* nomail.afraid.org (FromTheRafters)
Groupes : sci.mathDate : 29. Nov 2024, 09:54:10
Autres entêtes
Organisation : Peripheral Visions
Message-ID : <vibvfo$10t7o$1@dont-email.me>
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WM expressed precisely :
On 28.11.2024 20:28, FromTheRafters wrote:
WM used his keyboard to write :
On 28.11.2024 17:45, joes wrote:
Am Thu, 28 Nov 2024 11:39:05 +0100 schrieb WM:
>
A simpler arguments is this: All endsegments are in a decreasing
sequence.
There is no decrease, they are all infinite.
>
Every endsegment has one number less than its predecessor.
That is called decrease.
More like the subset relation. It is not a decrease in cardinality.
>
Of course not. Cardinality is nothing else than infinitely many.
Wrong, it is also 'number of elements' for finite sets.
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. You don't 'run out of indices' or elements to index.
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