Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 14. Dec 2024, 17:03:22
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vjka8a$1tms$4@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
User-Agent : Mozilla Thunderbird
On 14.12.2024 16:20, joes wrote:
Am Fri, 13 Dec 2024 09:54:12 +0100 schrieb WM:
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.
Why do you want to map N\D to N?
I don't. I show that it is impossible to map D to ℕ.
Regards, WM
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)