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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Andy Walker <anw@cuboid.co.uk>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Definition_of_real_number_=E2=84=9D_--infinitesimal?=
 =?UTF-8?Q?--?=
Date: Fri, 29 Mar 2024 12:39:17 +0000
Organization: Not very much
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On 28/03/2024 19:22, wij wrote:
> I saw lots of inconsistency in Andy Walker's response. I think the simple
> way to solve his doubt is for him to prove "repeating decimal is rational".
	Yet you cannot actually describe any inconsistency in what I [and for
that matter Fred, Richard, Keith and perhaps others] say.  My "doubt" is not
about what *I* know about mathematics, but about (a) your abuse of the terms
"R" and "real number" to describe mathematical objects to which you ascribe
properties which contradict the Archimedean axiom of R;  and (b) the lack of
any discernible rationale for your proposals.  So I ask again -- what problem
do Wij-numbers solve that use of the traditional real numbers fails to solve?

	There is no difficulty in evaluating a "repeating decimal" in R, and
the answer is easily seen to be rational.  If you hybridise R with some other
system which permits infinitesimals, then it's not surprising that you manage
to confuse yourself.

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