Re: .999... ?= 1

From: Virgil (ITSnetNOTcom/virgil_at_COMCAST.com)
Date: 06/11/04 

Date: Fri, 11 Jun 2004 12:45:50 -0600

In article <40C96A00.7060702@et.uni-magdeburg.de>,
 Eckard Blumschein <blumschein@et.uni-magdeburg.de> wrote:

> Robin Chapman wrote:
> > Johan Kullstam wrote:
>
> >>Not to be a smart ass, but what is a "number"? Is there some sort of
> >>generally agreed upon definition?
> >>
> > As I mentioned in another post: what systems are counted as "number systems"
> > is largely a historical accident. We generally regard the complexes
> > as "numbers" but generally not matrices or quaternions. In short
> > we know what rational numbers, real numbers etc. are, but "numbers" per
> > se are not defined. That doesn't stop Blumsheit from seeing some
> > essence of "number" such that "infinity" is one :-(
>
> I feel mistaken.
>
>
> Perhaps nobody will be able to seriously object against my objection
> that it does not make any sense in any practical application of a continuum
> to exclude a particular value as does mathematics for instance
> when it distinguishes between open and closed intervals.

No one requires the distiction between open and closed intervals to aply
to the physical world, but Eckwhatever has been complaining that when it
doe not, it signals a need to throw out what we have in the mathematical
world until csomething can be found which is a perfect match to that
physical world. That isn't how it is going to work.
>
> So what is wrong? People like David Rosenthal and Lothar Brendel who
> trust more in tenets they learned than in their own shallow reasoning
> feel great as an inquisitor: An outsider must be wrong.

This one certainly is.

> However, this does not resolve the problem. Do we really know what rational
> numbers are if numbers per se are not defined?

Rational numbers are quite adequately defined. Mathematicians know what
they are well enough. If Eckwhatever does not, that is his problem.
>
> Where might be a basic fallacy?

In assuming Eckwhatever knows what he is talking about?

> As long as we are not able to agree on
> the meaning of a number it might be premature to exclude the possibility
> that a continuum like Q and the natural numbers behave differently
> although they formally coincide in part.

In the first place, Q, if it meant to represent the set of rationals, is
not a continuum. Secondly, subsets already are allowed to behave
differently fron their supersets so mathematicians have not excluded
that possibility. If Eckwhatever has, that is his problem.
>
> I am suggesting a simple way out.

There is no "in" to get out of.

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