Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Julio Di Egidio <julio@diegidio.name>
Newsgroups: sci.math
Subject: Re: All infinities are countable in ordinary mathematics
Date: Tue, 6 May 2025 01:57:07 +0200
Organization: A noiseless patient Spider
Lines: 29
Message-ID: <vvbj8k$hkem$1@dont-email.me>
References: <vv7pv6$1rksi$1@dont-email.me>
 <oW6dnZu6VryWGIr1nZ2dnZfqnPednZ2d@giganews.com>
 <vv864c$1rksi$2@dont-email.me>
 <osqcnQQlLpd_LYr1nZ2dnZfqn_ednZ2d@giganews.com>
 <vv8etv$1rksi$3@dont-email.me>
 <3S-dnddWM4DLW4r1nZ2dnZfqn_ednZ2d@giganews.com>
 <vv8qv1$1rksi$4@dont-email.me>
 <DtGcnUIqYq65nIX1nZ2dnZfqnPqdnZ2d@giganews.com>
 <vv92bl$1rksj$1@dont-email.me> <vv92t3$1rksi$5@dont-email.me>
 <YY6cnTlzA-Ti3IX1nZ2dnZfqnPidnZ2d@giganews.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Tue, 06 May 2025 01:57:08 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="5bd6e37139f1e180703fb6e93d24bc3f";
	logging-data="578006"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18Og8dNPnOpWPDnhyJ4ynuCuH3KTT21ljA="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:B3QozvmuhBHClIjqhmPPwp+kaEM=
Content-Language: en-GB, it
In-Reply-To: <YY6cnTlzA-Ti3IX1nZ2dnZfqnPidnZ2d@giganews.com>
Bytes: 2625

On 05/05/2025 06:41, Ross Finlayson wrote:

> The idea though is that n/d makes standard infinitesimals
> even as if only in the, unbounded, the Archimedean.

....and war is peace, and freedom is getting a job...

> Then, if the un-countable, is not a constructivist result,
> is a point of contention, as that its proofs employ contradiction,
> and some constructivists have that's at odds with constructivism.

You are full of shit.  1) Diagonal arguments can be proved
constructively: ex falso quodlibet is not the same as
reductio ad absurdum: unless one deems ordinary induction
extra-ordinary, but that would be plain stupid.  OTOH,
2) the connection from binary sequences or subsets of the
natural numbers to real numbers is not immediate and not
granted, and not any more granted is uncountability.

Speaking of which, what do you even think this thread is
about??  THERE IS NO SUCH THING AS THE EXTRA-ORDINARY,
in ordinary and/or concrete (foundational!) mathematics:
so in any mathematics!  That's eventually my thesis.

Now try and give me a counter-example... that does not
rely on the real numbers being uncountable.

Julio