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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 16 Dec 2024 07:30:23 -0500
Organization: i2pn2 (i2pn.org)
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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.

> 
> Regards, WM
>>
>