Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
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
Lines: 56
Message-ID: <vlf1nu$17khf$11@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vksikk$17fjt$1@dont-email.me>
 <aa2941e93e806f1dda55d563dd062db67eb879f1@i2pn2.org>
 <vktmi3$1ia1u$1@dont-email.me>
 <c46775b30460bc564b3fe7bd1b838713829024f8@i2pn2.org>
 <vkv3t1$1qb93$1@dont-email.me>
 <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org>
 <vl1bp4$2bcos$2@dont-email.me>
 <4d797c9134ea480aa4976cf866cacaede8d309bd@i2pn2.org>
 <vl5uid$3au1p$1@dont-email.me> <vl650i$3c2ia$1@dont-email.me>
 <vl6il4$3ecap$5@dont-email.me>
 <1e8ebc58a12fd659e38d0b9f0ff6fc0194f933be@i2pn2.org>
 <vl88v4$3qtjc$5@dont-email.me>
 <ecf6965f78c9152b3fff0d3b18d7df0247100acf@i2pn2.org>
 <vl9605$3vk27$5@dont-email.me>
 <9a25e92033e0a4d24e9c27df0de95d8b033d0862@i2pn2.org>
 <vlasro$cr0k$1@dont-email.me>
 <a676a0802d5bdf15dd22a1f8cd5072893b6e1e33@i2pn2.org>
 <vldn14$vlah$2@dont-email.me>
 <171d790a8a99fa28e5b849e2726d1c9c0f93d932@i2pn2.org>
 <vlefcq$14esf$7@dont-email.me>
 <51593821cf96cef1e5f8c4d1cf692dc145064429@i2pn2.org>
 <vlenld$1686e$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 05 Jan 2025 23:39:59 +0100 (CET)
Injection-Info: dont-email.me; posting-host="0a9b3b8b2325ec9f2ae161f5c632ce0f";
	logging-data="1298991"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19bAlcMvOexS9dxxa8SlzoviMUAn5pGj1Q="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:E09SvjgmualPOWuDLZzOtSbupAY=
In-Reply-To: <vlenld$1686e$1@dont-email.me>
Content-Language: en-US
Bytes: 3804

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:|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.

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
>