Re: Definition of real number ℝ --infinitesimal--

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