Re: Cantor Diagonal Proof

Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

On Wed, 09 Apr 2025 14:11:54 +0000, Alan Mackenzie wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

On Tue, 08 Apr 2025 15:46:54 -0700, Keith Thompson wrote:

[ .... ]

If you're interested in learning more, search for "surreal numbers" or
"hyperreal numbers".  If you're not, don't.

Surreal numbers are bullshit as they don't actually exist, logically
(as I have show).  Bullshit can be internally consistent with itself.

What exactly do you mean by a mathematical entity "not existing"?  What
is your test which partitions such entities into "existing" and
"non-existing"?

/Flibble

Simple: things that make no logical sense don't exist: ....

Surreal numbers do make logical sense.  They form an ordered field which
has the real numbers as a subfield.

.... logically a real number always has a number smaller than it ....

Every stricly positive surreal number has a number smaller than it, too.

.... so trying to put a "surreal" infinitesimal on the same number line
as a "real" makes no logical sense: in fact I will go as far to say
that it is a category error.

The surreal number line is not the real number line, so trying to put a
surreal on the latter indeed makes no sense.  It might even constitute a
category error, as you suggest.

That, however, has no bearing on the existence of surreal numbers.  They
don't create inconsistencies, hence do exist, and have been studied
intensively.

/Flibble

--
Alan Mackenzie (Nuremberg, Germany).