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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
Date: Fri, 8 Nov 2024 12:05:40 -0500
Organization: i2pn2 (i2pn.org)
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On 11/8/24 11:43 AM, WM wrote:
> On 08.11.2024 13:28, Richard Damon wrote:
>> On 11/8/24 5:18 AM, WM wrote:
> 
>>> My understanding of mathematics and geometry is that reordering 
>>> cannot increase the measure (only reduce it by overlapping). This is 
>>> a basic axiom which will certainly be agreed to by everybody not 
>>> conditioned by matheology. But there is also an analytical proof: 
>>> Every reordering of any finite set of intervals does not increase 
>>> their measure. The limit of a constant sequence is this constant 
>>> however.
>>>
>>> This geometrical consequence of Cantor's theory has, to my knowledge, 
>>> never been discussed. By the way I got the idea after a posting of 
>>> yours: Each of {...,-3,-2,-1,0,1,2,3,...} is the midpoint of an 
>>> interval.
> 
>> which makes the error that the properties of finite objects apply to 
>> the infinite objects, which isn't true, and what just breaks your logic.
> 
> The infinite of the real axis is a big supply but an as big drain.

What "drain", the numbers exist.

>>
>> You take it as a given, but that just means that your logic is unable 
>> to actually handle the infinite.
> 
> I take it as evident that intervals of the measure 1/5 of the positive 
> real axis will not, by any shuffling, cover the real axis completely, 
> let alone infinitely often. I think who believes this is a deplorable 
> fanatic if not a fool.
> 
> Regards, WM
> 

Since 1/5 of infinity isn't a finite measure, you can't use finite logic 
to handle them.

You are just proving your use of broken logic.