Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!news.szaf.org!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail
From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Thu, 13 Mar 2025 17:04:12 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vqv36c$18mn$1@news.muc.de>
References: <vqrbtd$1chb7$2@solani.org> <vqrn89$u9t$1@news.muc.de> <vqrp47$2gl70$1@dont-email.me> <vqrtn3$1uq5$1@news.muc.de> <vqs1og$2k7oh$2@dont-email.me> <vqsh1r$2cnf$1@news.muc.de> <vqsoq5$2p6pb$1@dont-email.me> <vqsuf0$2g64$1@news.muc.de> <8734fghp5m.fsf@bsb.me.uk>
Injection-Date: Thu, 13 Mar 2025 17:04:12 -0000 (UTC)
Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2";
	logging-data="41687"; mail-complaints-to="news-admin@muc.de"
User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64))

Ben Bacarisse <ben@bsb.me.uk> wrote:
> Alan Mackenzie <acm@muc.de> writes:

>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 12.03.2025 18:42, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:

>>>>> If the numbers are definable.

>>>> Meaningless.  Or are you admitting that your "dark numbers" aren't
>>>> natural numbers after all?

>>> They

>> They?

>>>>> Learn what potential infinity is.

>>>> I know what it is.  It's an outmoded notion of infinity, popular in the
>>>> 1880s, but which is entirely unneeded in modern mathematics.

>>> That makes "modern mathematics" worthless.

>> What do you know about modern mathematics?  You may recall me challenging
>> others in another recent thread to cite some mathematical result where
>> the notion of potential/actual infinity made a difference.  There came no
>> coherent reply (just one from Ross Finlayson I couldn't make head nor
>> tail of).  Potential infinity isn't helpful and isn't needed anymore.

> WMaths does (apparently) have one result that is not a theorem of modern
> mathematics.  In WMaths there sets P and E such that

>   E in P   and   P \ {E} = P

> WM himself called this a "surprise" but unfortunately he has never been
> able to offer a proof.

Surprise indeed, but no surprise, too.  He's coming pretty close to
assertions like that in his replies to me, in the bits which are
coherent.

> On another occasion he and I came close to another when I defined a
> sequence of rationals that he agreed was monotonic, increasing and
> bounded above but which (apparently) does not converge to a real in
> WMaths.  It was "defined enough" to be monotonic and bounded but not
> "defined enough" to converge to a real.

Maybe it converged to some function of dark numbers.  They're not real,
are they?  ;-)  But he's clearly ignorant of the axiom of completion (the
one which distinguishes the reals from ordered subfields).

> But, in general, he hates talking about his WMaths because it gets him
> into these sorts of blind alleys.

But he loves going on about "dark numbers" and apparently still believes
they exist.  Hmmm.

> -- 
> Ben.

-- 
Alan Mackenzie (Nuremberg, Germany).