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Re: Paul Lutus says dumb things
Posted:
Dec 3, 2001 4:16 AM
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"Paul Lutus" <nospam@nosite.zzz> wrote in message
news://HYGO7.31980$tf5.1845402@bin5.nnrp.aus1.giganews.com...
> "The Scarlet Manuka" <sacha@maths.uwa.edu.au> wrote in message
> news://9ufcgh$ja9$1@fang.dsto.defence.gov.au...
> > "Paul Lutus" <nospam@nosite.zzz> wrote in message
> > news://OjGO7.51786$ox2.3639986@bin4.nnrp.aus1.giganews.com...
>
> > I said: The term "number system" is not well-defined, and it would be
> > unwise to define it in such a way as to exclude the extended real
numbers.
> I then made this specific claim about your specific remark and those of
> others:
> > > Assertions were made several times that the default number system
> > > is/was/should be one in which infinity is explicitly included,
> > > and this includes some of your own remarks.
Right. Something completely different.
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.
Does it help if I say that it would be equally unwise to define
"number system" in a way that would exclude Z, Q, R, C, or the
extended C?
That doesn't mean that I want extended C to be the default
number system; in fact I think that would be a very bad idea.
You still don't seem to recognise that there are lots of
different number systems out there, and wanting to define
"number system" so as to include all of those ones I
mentioned above doesn't mean that I want any particular
one of them to be set as a default.
> Again, since you are having such a tough time absorbing this, you had
said:
>
> > I said: The term "number system" is not well-defined, and it would be
> > unwise to define it in such a way as to exclude the extended real
numbers.
> The extended reals include +-infinity as members.
Yes, they do. That doesn't mean that my preferred default
number system has to, assuming I even have a preferred
default. It just means that I don't think axioms such as
additive cancellation should necessarily be applied to all
elements, any more than I think multiplicative cancellation
should be.
> do it for you. This most recent exchange has been positively schizoid.
Your
> assertions, and the denials of those assertions, almost fell on top of
each
> other.
Perhaps if you paid attention to what I'm actually saying,
rather than what you think I mean, you would realise that
I have not denied any of my assertions.
--
The Scarlet Manuka
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