Path: ...!feeds.phibee-telecom.net!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 07 Jun 2024 13:32:09 -0400
Organization: Peripheral Visions
Lines: 23
Message-ID: <v3vg6v$25k03$1@dont-email.me>
References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <f19c9718-9faf-4376-9c7d-5b0ec5ccce49@att.net> <5cjx16x9QcPy_u3MHizdiDCz_W8@jntp> <bd0ded55-16d4-454f-af12-896f024368d8@att.net> <bbfAzB76a9GzcAGShLauCHw3_MA@jntp> <5424f82c-1f04-43af-8963-3e325d797c8e@att.net> <vJvCxLOj98F4nrRmEh2M6dyGkSc@jntp> <v3su74$1k0sm$3@dont-email.me> <yIKqPz795F3VQXgdLfDbNosNLRc@jntp> <v3ups0$21poj$1@dont-email.me> <iHRrfHlPabW5zj1ZWCGH7OfulPA@jntp>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="utf-8"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 07 Jun 2024 19:32:16 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="91286aeb1ae9854e9b83d9f6f1c7a4b3";
	logging-data="2281475"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19e2+t7Yc3LfB2FvitZbFycEsGa1CUEf/I="
Cancel-Lock: sha1:2I44ZTPQucmlZXf+6Q9rb9mkbnI=
X-Newsreader: MesNews/1.08.06.00-gb
X-ICQ: 1701145376
Bytes: 2274

WM explained :
> Le 07/06/2024 à 13:10, Moebius a écrit :
>> Am 07.06.2024 um 13:01 schrieb WM:
>>> Le 06/06/2024 à 20:12, Moebius a écrit :
>>>> Am 05.06.2024 um 22:39 schrieb WM:
>>>>
>>>>  > most natural numbers are uncountable,
>
>> NO natural number is "uncountable"
>> 
>> Proof (by induction): 1 is "countable" (at least in my book). If n is 
>> "countable", then n+1 is "countable" too (again, at least in my book). 
>> Hence all natural numbers are "countable".
>
>
> Wrong. All numbers counted this way belong to a finite set*) upon which the 
> infinite set**) of uncountable numbers is following.
> ∀n ∈ ℕ_contable: |ℕ \ {1, 2, 3, ..., n}| = ℵo

Wrong! Every element of the natural numbers is countable (finite) and 
the entire set is countably infinite. You cannot change things by 
simply renaming your n-def as n-countable and pretend that they exist 
in N.