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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: Tue, 31 Dec 2024 10:44:37 -0500
Organization: i2pn2 (i2pn.org)
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On 12/30/24 4:41 PM, WM wrote:
> On 30.12.2024 17:11, Richard Damon wrote:
>> 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.
> 
>> Sure, if your threshold is n,
> 
> My threshold is not a fixed number but a potentially infinite set which 
> never grows to more than 1 % of ℕ. Proof: Every FISON that is multiplied 
> by 100 remains a FISON that can be multiplied by 100 without changing 
> this property.
> 
> Regards, WM
> 

Which shows that it isn't "a number", but one of an infinite set, and 
the set your are talking about is always a finite subset, and thus never 
the actual full set Natural Numbers or FISONs and thus your logic can't 
use the term every or all, because you can't actually USER every (only any).

Sorry, you are just proving that you are mentally incapable of handling 
the sets you are trying to talk about, because you are stuck in an 
insufficient logic that has exploded itself (and your understanding) to 
smithereens from the contradictions it runs into.

You just can't understand the infinite, because you seem to be missing 
the need piece of intelect.