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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 29 Nov 2024 16:37:30 +0100
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On 29.11.2024 14:57, Richard Damon wrote:
> On 11/29/24 8:44 AM, WM wrote:
>> On 29.11.2024 01:06, Richard Damon wrote:
>>> On 11/28/24 12:50 PM, WM wrote:
>>>> If for all intervals 1, 2, 3, ..., n the covering is 1/10, then 
>>>> there are no natnumbers outside of all intervals and there are no hats
>>>> outside of all intervals.
>>
>>> You are making the error of assuming that the infinite set is just 
>>> like a finite set that has part of it.
>>
>> No. Analysis concerns infinite sequences and sets.
> 
> You are looking at FINITE sets, and then trying to extrapolate to an 
> infinte set, which doesn't work.

Analysis is basic.
> 
>>>
>>> The problem is that the actual problem is defined on the INFINITE 
>>> set, and in that case, there ARE enough hats to cover.
>>
>> No. The limit of the sequence f(n) of relative coverings in (0, n] is 
>> 1/10, not 1. Therefore the relative covering 1 would contradict analysis.
> 
> And 0^x is 0, and x^0 is 1, which shows that just because you have a 
> constant sequence, it limit is not necessarily the final value.

The limit of the sequence 1/9, 1/9, 1/9, ... is 1/9.

Regards, WM