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From: "Chris M. Thomasson"
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
(extra-ordinary, effectively)
Date: Sun, 5 Jan 2025 14:39:58 -0800
Organization: A noiseless patient Spider
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On 1/5/2025 11:47 AM, WM wrote:
> 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:|â \ {1, 2, 3, ..., n}| = âľo.
>>>>>> 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 |â|.
>>> Find a FISON {1, 2, 3, ..., n} such that {1, 2, 3, ..., 100n} is a
>>> superset of â.
>
>> I never said there was,
>
> You said that I never used all FISONs. But I do. All are insufficient.
Have you thought about the following number:
(69^69^6969^696969^69696969^6969696969)+1
This is a number, just for men:
https://youtu.be/rVtHrgdcvZA
;^)
>
>> 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
>