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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 16 Dec 2024 13:21:22 -0800
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On 12/16/2024 4:30 AM, Richard Damon wrote:
> On 12/16/24 3:41 AM, WM wrote:
>> On 15.12.2024 21:32, joes wrote:
>>> Am Sun, 15 Dec 2024 12:25:26 +0100 schrieb WM:
>>>> 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.
>>> Which sequence do you get a limit of 0 from?
>>
>> Sorry, the limit of not indexed numbers is 9/10 according to analysis 
>> and 0 according to set theory, resulting in 9/10 = 0.
> 
> And that logic says that 1 is equal to 0.
> 
> 
>>>
>>>>>> 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.
>>> That sequence does not appear in the bijection.
>>
>> Therefore people were unaware of its failure.
> 
> YOU are unaware of YOUR failure as you have blown your brain out by your 
> logic's explosion to smithereens, leaving behind your darkness.

I think so. Damn. Shit happens.