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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Fri, 8 Nov 2024 19:05:04 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 08 Nov 2024 17:43:15 +0100 schrieb WM:
> 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.
What is the measure you are using and what does it give for the real
axis?

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.