Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 13. Dec 2024, 20:19:24
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vji1bs$3id0d$1@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
User-Agent : Mozilla Thunderbird
On 13.12.2024 19:29, joes wrote:
Am Fri, 13 Dec 2024 18:20:59 +0100 schrieb WM:
On 13.12.2024 15:41, joes wrote:
  > Am Fri, 13 Dec 2024 09:42:36 +0100 schrieb WM:
>
  >> The subset is considered as its own independent set D = {10n | n ∈
  >> ℕ}
  >> and then it is attached to the set ℕ = {1, 2, 3, ...}. That does not
  >> change the subset.
  > It changes the domain from D to N. What operation is „attachment”?
You can also say pairing. The elements of D are paired with the elements
10n of ℕ. After this small detour everything proceeds as usual.
Aha, and what is paired with the rest of N? This is not the identity.
I was under the impression the bijection step came later.
No, it came earlier and it was no bijecton.
Regards, WM
 

Date Sujet#  Auteur
13 Dec 24 * Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)5joes
13 Dec 24 `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)4WM
13 Dec 24  `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)3joes
13 Dec 24   `* Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)2WM
14 Dec 24    `- Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)1joes

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