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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: Sun, 5 Jan 2025 12:39:56 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <51593821cf96cef1e5f8c4d1cf692dc145064429@i2pn2.org>
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On 1/5/25 12:26 PM, WM wrote:
> On 05.01.2025 13:47, Richard Damon wrote:
>> On 1/5/25 5:31 AM, WM wrote:
>>> On 04.01.2025 11:59, joes wrote:
>>>> Am Sat, 04 Jan 2025 09:52:08 +0100 schrieb WM:
>>>>> On 04.01.2025 05:06, Richard Damon wrote:
>>>>>> On 1/3/25 12:15 PM, WM wrote:
>>>>>
>>>>>>> Every union of FISONs which stay below a certain threshold stays 
>>>>>>> below
>>>>>>> that threshold.
>>>>>> Every union of a finite number of FISONs is just an admssion that you
>>>>>> can't do the actual union of *ALL* FISONs.
>>>>> For all FISONs:|ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>> But not for the union.
>>>
>>> What should make the union larger than all FISONs?
>>>
>>> Every union of FISONs which stay below a certain threshold stays 
>>> belown that threshold.
>>
>> Because you never actually USED *ALL* FISONs,
> 
> All FISONs are smaller than 1 % of |ℕ|.
> Find a FISON {1, 2, 3, ..., n} such that {1, 2, 3, ..., 100n} is a 
> superset of ℕ.
> 
> Regards, WM
> 

I never said there was, but your claim doesn't match your conclusion, as 
the union of *ALL* the FISIONs will reach the size of the Natural 
Numbers, even though no finite subset reaches a measurable percentage of it.

That is just the nature of INFINITY, something that has been shown to be 
beyond your ability to understand.