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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 18:26:50 +0100
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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