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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 27 Nov 2024 09:17:25 -0500
Organization: i2pn2 (i2pn.org)
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On 11/27/24 6:10 AM, WM wrote:
> 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.
> 
> Assume that a bijection between natural numbers divisible by 10 and all 
> natural numbers is possible. First establish a bijection between the 
> numbers 10n ∈ ℕ and the numbers 10n ∈ D. This can be visualized by 
> attaching black hats to the natural numbers of the form 10n ∈ ℕ and 
> white hats to the remaining natural numbers. The black hats indicate 
> that a number n ∈ ℕ has a partner in D. Now it should be possible to 
> shift the black hats such that all natural numbers are covered by black 
> hats. The mapping f(10n) is started by exchanging white hats and black 
> hats precisely as would have been defined without the intermediate step: 
> 1 gets it from 10, 2 gets it from 20, 3 gets it from 30, and so on, 
> precisely as would be done without the intermediate first step.
> 
> However when all numbers of an interval (1, 2, 3, ..., n) are equipped 
> with black hats, then some black hats have been taken from outside of 
> the interval, from larger 10n which in turn have received white hats. If 
> all natural numbers are equipped with black hats, then all white hats 
> have disappeared. But hats cannot disappear by exchanging them.
> 
> Regards, WM
> 
> 

Just proves your funny-mental condition of being unable to understand 
that you need to follow the rules of the problem, and you have been 
sentence to life in the mathematical insane asylem where you brain has 
been exploded with the contradictions of your logic.