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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Thu, 13 Mar 2025 16:27:17 +0000
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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.

On another occasion he and I came close to another when I defines 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.

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

-- 
Ben.