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Re: Paul Lutus says dumb things
Posted:
Dec 3, 2001 3:22 PM
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Angus Rodgers <angus_prune@bigfoot.com> wrote:
> On Mon, 03 Dec 2001 17:29:39 GMT, "Paul Lutus"
> <nospam@nosite.zzz> wrote:
>
> > "The Scarlet Manuka" <sacha@maths.uwa.edu.au> wrote in message
> > news://9uffsa$nr8$1@fang.dsto.defence.gov.au...
> >
> > > I don't think that the extended reals would be a good default
> > > number system. You seem to insist that since I want them to be
> > > a number system, I want them to be the default. That is simply
> > > not true.
> >
> > You think there is no meaningful default definition for "number
> > system", a view not shared by many others, but you think if this
> > was feasible (on your own terms) than the extended reals should
> > be included in that definition.
>
> There are defaults, plural, and they are context-dependent.
That's an interesting, and perhaps fruitful, way of assessing the
situation. In other words, maybe you're thinking of N, Z, Q+, Q, R+,
R, R*, C, C*, etc. as all being sorts of defaults. I'm not sure that I
agree with calling them "context-dependent defaults", but maybe
something like that is reasonable. One thing, though, is certain:
If a single number system were ever to be accepted as "the default"
(and surely such a thing will never happen!), then context would
_very_ often cause automatic changes to systems other than the default.
A good example would be the question by the poster (a troll?) who
started this discussion in another thread. He said "... where 0 is
actually 1/infinity." Even if, say, the reals were somehow accepted
as "the default number system", the context established by that
poster's phrase would immediately throw us into an extended number
system of some sort.
> There is not one "number system". "Number system" is a class,
> one member of which is the extended system of real numbers.
>
> If The Scarlet Manuka had wanted to be hyper-precise, he might
> instead have said something like:
>
> The class "number system" is
> not well-defined, and it would be
> unwise to define it in such a way
> as to exclude the extended system
> of real numbers from membership.
Nicely put. To be hyper-precise though, there are two extensions of R,
the projective closure (1-pt. compactification) and the affine closure
(2-pt. compactification). Also, I have no reason to think that The
Scarlet Manuka is male, but perhaps you have better information in this
regard.
Cheers,
David Cantrell
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