> In article <cQtprmAna1C8EwLU@happybunny.jesus.cam.ac.uk>, > Simon Nickerson <email@example.com> wrote: > > > The situation with "infinity is not a number" is similar. At that level, > > it is *far* more important to persuade children that you can't treat > > infinity in the same way that you treat numbers like 3, 4.52 and -82.3 > > than it is to persuade them that it is sometimes useful to think of > > infinity as a member of the one-point compactification of the complex > > numbers. > > This is sci.math, not sci.math.children.
I think that he was explaining a common feature of the websites to which Paul Lutus has referred. They appear to be aiming at a lay audience, not a mathematically sophisticated audience. Hence, we may expect that they may sacrifice strict accuracy for the goal of pedagogy.
In simpler terms, I think that Simon was giving a reason to doubt that these web sites are authoritative on the question, "Is infinity a number?"
A silly question as far as I am concerned, and I take it that most posters of sci.math agree. The debate seems to be between one poster who confidently proclaims that infinity is not a number and other posters who suggest that there is no universally (or predominantly) accepted definition of number (or number system). Moreover, there are examples in which mathematicians use these terms which include infinity, so the negative answer is simply wrong.
-- Jesse Hughes
"Metaphysicians are musicians without musical ability." --Rudolf Carnap, "The Elimination of Metaphysics..."