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From: Andy Walker <anw@cuboid.co.uk>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Definition_of_real_number_=E2=84=9D?=
Date: Thu, 28 Mar 2024 15:59:06 +0000
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On 28/03/2024 13:16, Fred. Zwarts wrote:
> It seems that wij wants to define a number type that is different
> than the real numbers, but wij uses the same name Real. Very
> confusing.

	It seems to me to be worse than that.  Wij apparently thinks he
/is/ defining the real numbers, and that the traditional definitions are
wrong in some way that he has never managed to explain.  But as he uses
infinity and infinitesimals [in an unexplained way], he is breaking the
Archimedean/Eudoxian axiom, so Wij-reals are not R, and they seem also
not to be any of the other usual real-like number systems.  So the whole
of mathematical physics, engineering, ... is left in limbo, with all the
standard theorems inapplicable unless/until Wij tells us much more, and
probably not even then judging by Wij's responses thus far.

> Further, it seems he only defines how these number are written down.
> There is no explanation of how to interpret these writings.

	Well, quite.  It seems that we're supposed to use the standard
processes of arithmetic until we get to infinity and similar.  But of
course mathematics is concerned with numbers much more than with how
they are notated.

	All might become clear if Wij could explain what problem he is
really trying to solve.  What bridges fall down if "traditional" maths
is used but stay up with Wij-reals?  What new puzzles are soluble?  Are
they somehow more logical, or easier to teach?  He seems to think that
"trad" maths is full of holes that he sees but that all the great minds
of the past 2500 years have overlooked.  Perhaps it's all or mostly lost
in translation, but it's more likely that he is joining the PO Club.

-- 
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Couperin