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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 8 Nov 2024 17:43:15 +0100
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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.
> 
> 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