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NNTP-Posting-Date: Mon, 11 Nov 2024 19:00:29 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (doubling-spaces)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Mon, 11 Nov 2024 11:00:32 -0800
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On 11/11/2024 10:38 AM, Jim Burns wrote:
> On 11/11/2024 4:00 AM, WM wrote:
>> On 10.11.2024 21:36, Chris M. Thomasson wrote:
>>> On 11/10/2024 1:35 AM, WM wrote:
>>>> On 10.11.2024 00:27, Jim Burns wrote:
>>>>> On 11/9/2024 6:45 AM, WM wrote:
>
>>>>>> Everybody who believes that the intervals
>>>>>> I(n) = [n - 1/10, n + 1/10]
>>>>>> could grow in length or number
>>>>>> to cover the whole real axis
>>>>>> is a fool or worse.
>>>>>
>>>>> Our sets do not change.
>>
>> But intervals on the real axis can be translated.
>
> The interval [4-⅒,4+⅒] can be translated to
> the interval [1/3-⅒,1/3+⅒].
>
> [4-⅒,4+⅒] does not change to [1/3-⅒,1/3+⅒]
> [4-⅒,4+⅒] will continue being after translation.
> [1/3-⅒,1/3+⅒] has never been [4-⅒,4+⅒].
>
> Our sets do not change.
> Everybody who believes that
>   intervals could grow in length or number
> is deeply mistaken about
>   what our whole project is.
>
>

How about Banach-Tarski equi-decomposability?