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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 18 Dec 2024 12:25:25 +0100
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On 18.12.2024 11:16, Mikko wrote:
> On 2024-12-17 19:29:52 +0000, WM said:
> 
>> On 17.12.2024 14:08, Mikko wrote:
>>> On 2024-12-16 11:04:17 +0000, WM said:
>>>
>>>>> False. Regardless which interval is "the" interval the distance to 
>>>>> that
>>>>> interval is finite and the length of the interval is non-zero so the
>>>>> ratio is finite.
>>>>
>>>> Well, it is finite but huge. Much larger than the interval and 
>>>> therefore the finite intervals are not dense.
>>>
>>> They are dense because there are other intervals between the point 
>>> and the
>>> interval.
>>
>> The distance between intervals (in some location) is finite but much, 
>> much larger than the finite length of the interval. This distance is 
>> the distance between intervals which are next to each other. Therefore 
>> there is nothing in between.
> 
> There is no next interval and therefore no distance to the next interval
> as there are always other intervals nearer.

Mathematics says the covering by intervals is 3/oo. Therefore the ratio 
between not covered part and covered part of the positive real axis is 
oo/3. That implies an average of oo/3 which in some locations must be 
realized.

That proves the existence of distances between next intervals much 
larger than the finite lengths of the intervals. It excludes density of 
intervals.
> 
> You haven't prove your claim and can't prove so it is just an unujustified
> opnion.

Above a mathematician can find a sober mathematical derivation.

Regards, WM