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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, 1 Dec 2024 11:55:15 +0100
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On 01.12.2024 11:17, Mikko wrote:
> On 2024-11-27 11:10:51 +0000, WM said:
> 
>> On 27.11.2024 10:33, Mikko wrote:
>>> On 2024-11-26 11:07:57 +0000, WM said:
>>>
>>>> On 26.11.2024 10:09, Mikko wrote:
>>>>> On 2024-11-25 14:38:13 +0000, WM said:
>>>>
>>>>>> The simple example contradicts a bijection between the two sets 
>>>>>> described above.
>>>>>
>>>>> What does "contradicts a bijection" mean?
>>>>>
>>>> It shows that the mapping claimed to be a bijection is not a bijection.
>>>
>>> If so, no bijection is contradicted.
>>
>> The possibility of a bijection between the sets  ℕ = {1, 2, 3, ...} 
>> and D = {10n | n ∈ ℕ} is contradicted.
> 
> No, it is not. You merely deny it, disregarding obvious facts.

Obvious is that for every interval (0, n] the relative covering is 1/10, 
and that there are no further black hats beyond all natnumbers n.

> The function
> f(x) = 10 * f obviously maps every element of ℕ to a different element of
> D and there is no element of D that is not 10 * f for some f so this f is
> a bijection between ℕ and D.

It appears so. I have shown by a different example that it is wrong. The 
relative covering for every interval is 1/10, independent of the 
configuration of the hats available inside. The limit of this sequence 
is 1/10.

Regards, WM