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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 15 Dec 2024 12:25:26 +0100
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On 15.12.2024 11:56, Mikko wrote:
> On 2024-12-14 08:53:19 +0000, WM said:

>> Please refer to the simplest example I gave you on 2024-11-27:
>> The possibility of a bijection between the sets ℕ = {1, 2, 3, ...} and 
>> D = {10n | n ∈ ℕ} is contradicted because for every interval (0, n] 
>> the relative covering is not more than 1/10, and there are no further 
>> numbers 10n beyond all natural numbers n.
> 
> It is already proven that there is such bijection. What is proven cannot
> be contradicted unless you can prove that 1 = 2.

What is proven under false (self-contradictory) premises can be shown to 
be false. Here we have a limit of 1/10 from analysis and a limit of 0 
from set theory. That shows that if set theory is right, we have
1/10 = 0 ==> 1 = 0 ==> 2 = 1.
> 
>> The sequence 1/10, 1/10, 1/10, ... has limit 1/10.
> 
> Irrelevant as the proof of the exitence of the bijection does not
> mention that sequence.

But the disproof of the bijection does. There is no reason to forbid 
that sequence.

Regards, WM
>