Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 17. Nov 2024, 08:50:07
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhc77g$hdd4$1@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 16.11.2024 23:36, Jim Burns wrote:
On 11/16/2024 2:54 PM, WM wrote:
Therefore
the set of intervals cannot grow.
An infinite set can match a proper superset
without growing.
But with shrinking. When it matches first itself and then a proper subset, then it has decreased. The set of even numbers has fewer elements than the set of integers.
Because it is infinite.
The interval [0, 1] is infinite because it can be split into infinitely many subsets. But its measure remains constant. There is no reason except naivety to believe that the intervals [n - 1/10, n + 1/10] could cover the real line infinitely often.
Regards, WM
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