Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Mon, 14 Apr 2025 17:49:56 -0700
Organization: None to speak of
Lines: 34
Message-ID: <878qo22qq3.fsf@nosuchdomain.example.com>
References: <vsn1fu$1p67k$1@dont-email.me> <vsuvp1$227l5$1@dont-email.me>
	<vsvv3h$36pju$2@dont-email.me> <vt01u5$38f07$1@dont-email.me>
	<875xjfd5rs.fsf@nosuchdomain.example.com>
	<vt1jpa$n43m$4@dont-email.me>
	<87tt6zblzl.fsf@nosuchdomain.example.com>
	<0920ac6e196c1cebeff36d8b9431ee12a7b3d527@i2pn2.org>
	<vt74k1$1pl6i$5@dont-email.me>
	<74db303c1d07ba0fdf70f1b20f5f7d6e04667665@i2pn2.org>
	<vt9nr3$5t7s$5@dont-email.me>
	<4f2f706fdbd8bb237b4bfbc750f65482db6e96c7@i2pn2.org>
	<vtag8u$vqm0$3@dont-email.me>
	<c7320364d5ad63cd30018fa0082e8dcc60ad2534@i2pn2.org>
	<vtc4ao$2mlfb$4@dont-email.me>
	<84c84545ad9509384f5378553217346b12512a97@i2pn2.org>
	<vtha1c$3oh15$2@dont-email.me>
	<87h62rg1rx.fsf@nosuchdomain.example.com> <vthjd4$4lt$1@dont-email.me>
	<87cydffviw.fsf@nosuchdomain.example.com>
	<vtk2vs$295ku$5@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 15 Apr 2025 02:50:01 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="a2350407d780bb528cb106f4e5e26372";
	logging-data="2640926"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+wlL2iYRgao0liAoRxwdFr"
User-Agent: Gnus/5.13 (Gnus v5.13)
Cancel-Lock: sha1:SMKgrTzURmvwofEMZ0KdGR5sWXQ=
	sha1:xqR9CTGQ6iYSR1uTOfpjXgDjCqI=
Bytes: 3124

Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> On Sun, 13 Apr 2025 17:15:35 -0700, Keith Thompson wrote:
>
>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>>
>>> On Sun, 13 Apr 2025 15:00:34 -0700, Keith Thompson wrote:
>>>>
>>>> The Cantor construction *assumes* the existence of such a list ...
>>>
>>> Clearly, then, there must not be any objections to the creation of such
>>> a list, other than the Cantor construction itself.
>> 
>> Why would you assume that?
>
> Because I don’t see any objections to Cantor making that assumption.

What assumption?

Cantor did not assume that there are no objections to the creation
of such a list, other than the Cantor construction itself.  Cantor
started by assuming the existence of such a list, and showed that
that assumption leads to a contradiction, thereby proving that no
such list exists.  There's no reason to think that there couldn't
be other proofs of the nonexistence of such a list.

Do you question the validity of reductio ad absurdum?

I asked questions in my previous article; you snipped them.
If you're going to do continue doing that, I won't waste more time
discussing this with you.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */