Re: The non-existence of "dark numbers"

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.