"The Scarlet Manuka" <sacha@maths.uwa.edu.au> wrote in message news://9ufase$o2o$1@fang.dsto.defence.gov.au...
> You seem to have a large problem with comprehension.
No, your problem is that I understand what you are saying. Based on the content of your posts, this is a risk you had not planned on taking.
> 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.
Then stop denying that this is your claim. You cannot simultaneously deny that this claim has been made, by you and others, and yet make it every other line.
The above statement is that the default meaning of "number system" is or should be one identical to the extended reals.
> There *is* *no* commonly presented meaning of "number system". It is > not a formally defined term. At most, some examples are presented.
Apart form being false, this hasn't stopped you from asserting a preferred definition for it, which appears above.
In fact, the prevailing definition is provided implicitly in each and every one of the Web pages in my list. Each page that says "infinity is not a number" (i.e. all of them) is making a statement about the default number system -- it excludes infinity. Why is it the default? Because (1) the statement is uniform, without significant variation, and (2) no qualification of "number" is made, except to say it constitutes a set that excludes infinity.
Alternative? All those educators are spouting nonsense, at the expense of their students (and their careers). Which explanation do you think is most likely?
