"Paul Lutus" <firstname.lastname@example.org> wrote in message news://HYGO7.email@example.com... > "The Scarlet Manuka" <firstname.lastname@example.org> wrote in message > news://email@example.com... > > "Paul Lutus" <firstname.lastname@example.org> wrote in message > > news://OjGO7.email@example.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.