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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: Wed, 20 Nov 2024 12:42:15 +0100
Organization: A noiseless patient Spider
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On 19.11.2024 17:26, Jim Burns wrote:
> On 11/19/2024 6:01 AM, WM wrote:

>> That implies that
>> our well-known intervals
> 
> Sets with different intervals are different.
> Our sets do not change.

The intervals before and after shifting are not different. Only their 
positions are.

Is the set {1} different from the set {1} because they have different 
positions? Is the set {1} in 1, 2, 3, ... different from the set {1} in 
-oo, ..., -1, 0, 1,... oo?

> Sets of our well.known.intervals
> can match some proper supersets without growing 

They cannot match the rational numbers without covering the whole 
positive real line. That means the relative covering has increased from 
1/5 to 1.

> Relative covering isn't measure.

It is a measure! For every finite interval between natural numbers n and 
m the covered part is 1/5.

> You haven't defined 'relative covering'.
> Giving examples isn't a definition.

If you are really too stupid to understand relative covering for finite 
intervals, then I will help you. But I can't believe that it is 
worthwhile. Your only reason of not knowing it is to defend set theory 
which has been destroyed by my argument.

> I claim that there are functions f:ℝ→ℝ
> such that
> ⟨ f(⅟1) f(⅟2) f(⅟3) ... ⟩  =
> ⟨ ⅟5    ⅟5    ⅟5    ... ⟩
> and  f(0)  =  1

Not in case of geometric shifting. All definable intervals fail in all 
definable positions.
> 
>> So you deny analysis or / and geometry.
> 
> I deny what you think analysis and geometry are.
> I accept infinite sets
> and discontinuous functions

Discontinuity is not acceptable in the geometry of shifting intervals.
> What is it you (WM) accuse infinite sets of,
> other than not being finite?

Nothing against infinite sets. I accuse matheologians to try to deceive.
> 
> Note:
> An infinite set
> can match some proper supersets without growing

I have proven that this is nonsense.

Regards, WM