Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 13. Dec 2024, 09:54:12
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vjgsnk$3a54o$2@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 13.12.2024 03:29, Richard Damon wrote:
On 12/12/24 4:57 PM, WM wrote:
D = {10n | n ∈ ℕ} is the set being mapped. The set D being mapped does not change when it is attached to the set ℕ being mapped in form of black hats.
And so, which element of which set didn't get mapped to a member of the other by the defined mapping?
No such element can be named. But 9/10 of all ℕ cannot get mapped because the limit of the constant sequence 1/9, 1/9, 1/9, ... is 1/9. This proves the existence of numbers which cannot be named.
Regards, WM
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