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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: Tue, 12 Nov 2024 17:43:32 +0100
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On 12.11.2024 16:58, Jim Burns wrote:
> On 11/11/2024 3:33 PM, WM wrote:
>> On 11.11.2024 19:23, Jim Burns wrote:
>>> On 11/11/2024 3:41 AM, WM wrote:
> 
>>>> My intervals I(n) = [n - 1/10, n + 1/10]
>>>> must be translated to all the midpoints
>>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5,
>>>> 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1, ...
>>>> if you want to contradict my claim.
>>>
>>> Your 𝗰𝗹𝗮𝗶𝗺𝘀 start with "Sets change".
>>
>> No, I claim that intervals can be translated.
> 
> By which, you mean that translation changes intervals.

No, the intervals remain constant in size and multitude.

>> (The set of intervals remains constant
>> in size and multitude.)
> 
> The set of intervals remains constant. Absolutely.
> Sets do not change.
> Intervals do not change.
> Mathematical objects do not change.

Therefore the intervals covering all naturals cannot cover more. But the 
rationals are more in the sense that they include all naturals and 1/2. 
By your argument Cantor has been falsified.

Regards, WM

Regards, WM