Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Tue, 25 Mar 2025 17:05:00 +0100
Organization: A noiseless patient Spider
Lines: 41
Message-ID: <vruk7d$3l4i0$1@dont-email.me>
References: <vqrbtd$1chb7$2@solani.org> <vrhrlb$3ta8t$1@dont-email.me>
 <c0de7504-7d17-42f1-83e8-8767c0859c0c@att.net> <vrj5nh$12273$1@dont-email.me>
 <efbe60c5-6691-4fd6-8638-589fd95ec8a4@att.net> <vrkabi$233at$1@dont-email.me>
 <vrkca8$18dh$1@news.muc.de> <vrlt7r$3hfcp$3@dont-email.me>
 <vrmg0s$308h$1@news.muc.de> <vrmibq$5e2r$1@dont-email.me>
 <vrmj7b$5e2s$1@dont-email.me> <vrmkv7$308h$3@news.muc.de>
 <vrpn1k$3002f$2@dont-email.me> <vrpo23$po9$1@news.muc.de>
 <vrsdbt$1gv1c$3@dont-email.me> <vrsec9$1lg8$1@news.muc.de>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Tue, 25 Mar 2025 17:05:01 +0100 (CET)
Injection-Info: dont-email.me; posting-host="3da338aa076d1cb1638e1bf364f94e88";
	logging-data="3838528"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19eQX9v4JYcJ+5CyrTbU6zLAn8ePvTBFUw="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:Fc9XxIWivtzFybIM1ouxfL9HaBs=
Content-Language: en-US
In-Reply-To: <vrsec9$1lg8$1@news.muc.de>
Bytes: 3001

On 24.03.2025 21:12, Alan Mackenzie wrote:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> On 23.03.2025 20:39, Alan Mackenzie wrote:
>>> You did not, in your
>>> voluminous post, cite any indication of a _use_ of "potentially
>>> infinite", only some philosophising about it.
> 
>> Have you not read Hilbert and Cantor? In analysis potential infinity and
>> only it is used.
> 
> What is used is the infinite.  It needs no redundant qualifier
> "potential".

You don't grasp it.
> 
> You have dishonestly snipped the core of my last post.  Here it is
> again:
> 
>>> In modern mathematics there are the notions finite and infinite.  They
>>> are useful.  I challenge you to produce a theorem which cannot be proven
>>> with those notions, yet can be proven with, additionally, "potentially
>>> infinite".

I told you that all mathematics is based on potential infinity.
> 
>>> If neither you nor anybody else can do this, then we must conclude that
>>> "potentially infinite" has no use in mathematics.

Actual infinity has no use in any kind of applied mathematics.

>> In fact all meaningful and correct applications of infinity in
>> mathematics concern potential infinity, because actual infinity either
>> is a chimera only or it is dark and therefore cannot be manipulated and
>> applied in mathematics.
> 
> "Potential infinity", I repeat, is unnecessary,

Try to understand the scholars I quoted.

Regards, WM