Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

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 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".

If neither you nor anybody else can do this, then we must conclude that
"potentially infinite" has no use in mathematics.

Can I take it that you cannot meet that challenge, and you know of no use
of "potential infinity" which would justify its existence in the sense of
my previous two paragraphs?

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, given the well defined
notions of "finite" and "infinite".  It only introduces confusion.

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).