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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Sun, 5 Jan 2025 20:47:57 +0100
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On 05.01.2025 18:39, Richard Damon wrote:
> 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.

> I never said there was,

You said that I never used all FISONs. But I do. All are insufficient.

> 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.
> 
How do they do it? Do one or more FISONs grow during the union process? 
(One would be sufficient.)

Regards, WM