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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: Tue, 17 Dec 2024 07:34:07 -0500
Organization: i2pn2 (i2pn.org)
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On 12/17/24 4:05 AM, WM wrote:
> On 16.12.2024 18:25, joes wrote:
>> Am Mon, 16 Dec 2024 17:49:20 +0100 schrieb WM:
>>> On 16.12.2024 16:40, joes wrote:
>>>> Am Mon, 16 Dec 2024 14:59:27 +0100 schrieb WM:
>>>>> On 16.12.2024 12:55, joes wrote:
>>>>>> Am Mon, 16 Dec 2024 09:30:18 +0100 schrieb WM:
>>>>>
>>>>>>> All intervals do it because there is no n outside of all intervals
>>>>>>> [1, n]. My proof applies all intervals.
>>>>>> It does not. It applies to every single finite „interval”,
>>>>> What element is not covered by all intervals that I use?
>>>>>> but not to the whole N.
>>>> You do not cover N, only finite parts.
>>> What do I miss to cover?
>> Inf.many numbers for every n.
> 
> But Cantor using every n does not miss to cover anything?
> 
>  > N is infinite.
> 
> Every element is the last element of a FISON [1, n]. ℕ is the set of all 
> FISONs. I use all FISONs. ∀n ∈ ℕ: f([1, n]) =< 1/10.
> Ever heard of the effect of the universal quantifier?
> 
> Regards, WM
> 
> Regards, WM
> 

But your logic can't deal with ALL Fisons.

Note, the mapping isn't in your [1, n] but in N.

Your logic that if it holds for all FISONs, it holds for N, is what 
shows that 0 == 1, so we see that logic is broken when it is applied to 
truely infinite things.