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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Mon, 30 Dec 2024 11:11:07 -0500
Organization: i2pn2 (i2pn.org)
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On 12/30/24 3:50 AM, WM wrote:
> On 30.12.2024 01:39, Richard Damon wrote:
>> On 12/29/24 12:53 PM, WM wrote:
>>> On 29.12.2024 13:34, Richard Damon wrote:
>>>> On 12/29/24 6:01 AM, WM wrote:
>>>
>>>>>
>>>>> All definable numbers (FISONs) stay below 1 %. Every union of 
>>>>> "below 1 %" stays below 1 %.
>>>>
>>>> Since 0 is Less than 1, you are sort of correct, but that fact 
>>>> doesn't prove your claim.
>>>>
>>>> The problem is that when you get to *ALL* 
>>>
>>> I get to all FISONs below a certain threshold, namely a threshold 
>>> between which and ω there exist ℵ₀ natnumbers.
>>>
>> Which isn't "All FISONs"
> 
> Do you personally know FISONs larger than those? Please let me know them.
> 
> Regards, WM
> 

Sure, if your threshold is n, then the fision from 1 to n+1 is bigger 
than that. and from there you can get to n+2, then n+3, and can start to 
understand what happens as you get to infinity.

Of course, to do that, you need to abandon the concept that you are only 
working with SOME of the set, and not ALL of it, and thus there isn't a 
"last" element, as the set is infinite.