Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 21. Nov 2024, 17:24:51
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vhnmsi$n2pc$1@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 21.11.2024 16:39, Jim Burns wrote:
On 11/21/2024 5:21 AM, WM wrote:
That means the function describing this,
1/10, 1/10, 1/10, ...
has limit 1/10.
That is the quotient of
the infinity of black intervals and
the infinity of all intervals.
The Paradox of the Discontinuous Function
(not a paradox):
It is a paradox that only 1/10 of the real line is covered for every finite interval (0, n] but all is covered completely in the limit. By what is it covered, after all n have been proved unable?
lim.⟨ rc(1), rc(2), rc(3), ... ⟩ ≠
rc( lim.⟨ 1, 2, 3, ... ⟩ )
You (WM) do not "believe in"
proper.superset.matching sets
discontinuous functions
There is no reason to believe in magic. But if you do, then all Cantor-bijections can fail as well "in the infinite". Then mathematics is insufficient to determine limits.
Regards, WM
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