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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Definition_of_real_number_=E2=84=9D_--infinitesimal?=
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Date: Thu, 28 Mar 2024 11:07:30 -0500
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On 3/28/2024 10:59 AM, Andy Walker wrote:
> 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.
> 

Yet it seems that wij is correct that 0.999... would seem to
be infinitesimally < 1.0. One geometric point on the number line.
[0.0, 1.0) < [0.0, 1.0] by one geometric point.

>> 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.
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer